Transcript: Circles_20250702_134128.html

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[
  {
    "slide": 1,
    "fragments": [
      {
        "fragment_index": 1,
        "text_description": "What is a Circle?",
        "image_description": ""
      },
      {
        "fragment_index": 2,
        "text_description": "Circle",
        "image_description": ""
      },
      {
        "fragment_index": 3,
        "text_description": "A circle is the set of all points in a plane equidistant from one fixed point called the centre. That constant distance is the radius.\nExample: if each point is 5 cm from the centre, the radius is 5 cm.",
        "image_description": ""
      }
    ]
  },
  {
    "slide": 2,
    "fragments": [
      {
        "fragment_index": -1,
        "text_description": "Chord vs Arc",
        "image_description": ""
      },
      {
        "fragment_index": 1,
        "text_description": "Straight chord (blue) and corresponding curved arc (red)",
        "image_description": "https://asset.sparkl.ac/pb/sparkl-vector-images/img_ncert/d5lzBKG88XcsXm0abTLbItaITBXKdSPdoROcDK6f.png"
      },
      {
        "fragment_index": 2,
        "text_description": "How are they different?\nA chord is a straight line segment that directly connects two points on a circle.\nAn arc is the curved part of the circle's circumference between the same two points.\nKey Points:\nChord: straight, lies inside the circle.\nArc: curved, sits on the circumference.\nBoth share the same endpoints.",
        "image_description": ""
      }
    ]
  },
  {
    "slide": 3,
    "fragments": [
      {
        "fragment_index": -1,
        "text_description": "Name the Parts\nDrag each label onto the circle to prove you know the centre, radius, diameter, chord and arc.\nResults\n// Drag and drop functionality\n        const draggableItems = document.querySelectorAll('.draggable-item');\n        const dropZones = document.querySelectorAll('.drop-zone');\n        const checkAnswersBtn = document.getElementById('checkAnswersBtn');\n        const feedbackArea = document.getElementById('feedbackArea');\n        const feedbackContent = document.getElementById('feedbackContent');\n        \n        // Drag and drop event listeners\n        draggableItems.forEach(item => {\n            item.addEventListener('dragstart', handleDragStart);\n            item.addEventListener('dragend', handleDragEnd);\n        });\n        \n        dropZones.forEach(zone => {\n            zone.addEventListener('dragover', handleDragOver);\n            zone.addEventListener('drop', handleDrop);\n            zone.addEventListener('dragenter', handleDragEnter);\n            zone.addEventListener('dragleave', handleDragLeave);\n        });\n        \n        function handleDragStart(e) {\n            e.target.classList.add('opacity-50');\n            e.dataTransfer.setData('text/plain', e.target.dataset.id);\n        }\n        \n        function handleDragEnd(e) {\n            e.target.classList.remove('opacity-50');\n        }\n        \n        function handleDragOver(e) {\n            e.preventDefault();\n        }\n        \n        function handleDragEnter(e) {\n            e.preventDefault();\n            e.target.closest('.drop-zone').classList.add('border-green-500', 'bg-green-50');\n        }\n        \n        function handleDragLeave(e) {\n            e.target.closest('.drop-zone').classList.remove('border-green-500', 'bg-green-50');\n        }\n        \n        function handleDrop(e) {\n            e.preventDefault();\n            const dropZone = e.target.closest('.drop-zone');\n            dropZone.classList.remove('border-green-500', 'bg-green-50');\n            \n            const itemId = e.dataTransfer.getData('text/plain');\n            const draggedItem = document.querySelector(`[data-id=\"${itemId}\"]`);\n            \n            if (draggedItem && dropZone && !dropZone.querySelector('.draggable-item')) {\n                dropZone.appendChild(draggedItem);\n                dropZone.querySelector('.text-center').style.display = 'none';\n            }\n        }\n        \n        // Check answers functionality\n        checkAnswersBtn.addEventListener('click', () => {\n            const correctMap = {\n                \"zone-1\": \"item-centre\",\n                \"zone-2\": \"item-radius\",\n                \"zone-3\": \"item-diameter\",\n                \"zone-4\": \"item-chord\",\n                \"zone-5\": \"item-arc\"\n            };\n            \n            let score = 0;\n            Object.keys(correctMap).forEach(zoneId => {\n                const zone = document.querySelector(`[data-id=\"${zoneId}\"]`);\n                const item = zone.querySelector('.draggable-item');\n                if (item && item.dataset.id === correctMap[zoneId]) {\n                    zone.classList.add('border-green-400');\n                    score++;\n                } else {\n                    zone.classList.add('border-red-400');\n                }\n            });\n            \n            feedbackArea.classList.remove('hidden');\n            feedbackContent.innerHTML = `<p class=\"text-gray-800\">You labelled ${score} out of 5 parts correctly.</p>`;\n        });",
        "image_description": ""
      },
      {
        "fragment_index": 1,
        "text_description": "Draggable Items\nCentre\nRadius\nDiameter\nChord\nArc",
        "image_description": ""
      },
      {
        "fragment_index": 2,
        "text_description": "Drop Zones\nDrop here\nDrop here\nDrop here\nDrop here\nDrop here",
        "image_description": ""
      },
      {
        "fragment_index": 3,
        "text_description": "Tip:\nThe radius is always half the diameter—use that fact to place both labels correctly.",
        "image_description": ""
      },
      {
        "fragment_index": 4,
        "text_description": "Check Answers",
        "image_description": ""
      }
    ]
  },
  {
    "slide": 4,
    "fragments": [
      {
        "fragment_index": -1,
        "text_description": "Angles: Centre vs Rim",
        "image_description": ""
      },
      {
        "fragment_index": 1,
        "text_description": "Central and inscribed angles on the same arc",
        "image_description": "https://asset.sparkl.ac/pb/sparkl-vector-images/img_ncert/WKb5UGd4DZiN9jOBD9HnKom8Jj0PdyzLmNnWglgH.png"
      },
      {
        "fragment_index": 2,
        "text_description": "Angle at Centre Theorem\nAngle at Centre Theorem states: the central angle on an arc equals twice the inscribed angle on that arc.\nSo if the central angle measures \\(2x^\\circ\\), the corresponding rim angle is \\(x^\\circ\\).\nKey Points:\nCentral angle \\( \\angle AOB = 2x^\\circ \\).\nInscribed angle \\( \\angle ACB = x^\\circ \\).\nBoth subtend arc \\( \\overset{\\frown}{AB} \\); ratio is always 2 : 1.",
        "image_description": ""
      }
    ]
  },
  {
    "slide": 5,
    "fragments": [
      {
        "fragment_index": -1,
        "text_description": "Sector and Segment\nSpot the Difference",
        "image_description": ""
      },
      {
        "fragment_index": 1,
        "text_description": "Sector (slice) vs Segment (crust)",
        "image_description": "https://asset.sparkl.ac/pb/sparkl-vector-images/img_ncert/R0qS4MbrNIcMFJtpysLj5tggBqDrMNXNDChqD44u.png"
      },
      {
        "fragment_index": 2,
        "text_description": "Sector: region bounded by two radii and the arc they enclose—like a pizza slice.",
        "image_description": ""
      },
      {
        "fragment_index": 3,
        "text_description": "Segment: region bounded by a chord and the arc between its endpoints—just the crust part.",
        "image_description": ""
      },
      {
        "fragment_index": 4,
        "text_description": "Key Points:\nSector boundary: 2 radii + arc.\nSegment boundary: chord + arc.\nCentre lies in every sector, rarely in a segment.",
        "image_description": ""
      }
    ]
  },
  {
    "slide": 6,
    "fragments": [
      {
        "fragment_index": -1,
        "text_description": "Key Formulas",
        "image_description": ""
      },
      {
        "fragment_index": 1,
        "text_description": "\\[ C = 2\\pi r,\\;\\; A = \\pi r^{2} \\]\nThese two expressions give a circle’s circumference and area. Both increase directly with radius \\(r\\).",
        "image_description": ""
      },
      {
        "fragment_index": 2,
        "text_description": "Variable Definitions\n\\(C\\)\nCircumference\n\\(A\\)\nArea\n\\(r\\)\nRadius of the circle\n\\(\\pi\\)\nConstant  (\\(\\approx 3.14\\))",
        "image_description": ""
      },
      {
        "fragment_index": 3,
        "text_description": "Applications\nTrack distance\nUse \\(C\\) to find how far a wheel rolls in one turn.\nCover circular surfaces\nUse \\(A\\) to estimate paint, seeds, or fabric needed.\nConvert diameter & radius\nKnowing \\(r\\) links all circle measurements quickly.",
        "image_description": ""
      }
    ]
  },
  {
    "slide": 7,
    "fragments": [
      {
        "fragment_index": -1,
        "text_description": "Arc Length Formula",
        "image_description": ""
      },
      {
        "fragment_index": 1,
        "text_description": "Sector with radius r and central angle θ.",
        "image_description": "https://asset.sparkl.ac/pb/sparkl-vector-images/img_ncert/HyzmhZcXTPMsi8QTfVGeTYSmGnUWLQE9duaBJslT.png"
      },
      {
        "fragment_index": 2,
        "text_description": "Relating Angle, Radius & Arc\nFormula: \\(s = 2\\pi r \\times \\frac{\\theta}{360^\\circ}\\).\nArc length \\(s\\) equals the full circumference scaled by the angle fraction.",
        "image_description": ""
      },
      {
        "fragment_index": 3,
        "text_description": "Key Points:\nArc length is proportional to the central angle \\(\\theta\\).\nIt grows directly with radius \\(r\\).\nProportional reasoning: part = whole \\((2\\pi r)\\) × angle fraction.",
        "image_description": ""
      }
    ]
  },
  {
    "slide": 8,
    "fragments": [
      {
        "fragment_index": -1,
        "text_description": "Play with Arc Length",
        "image_description": ""
      },
      {
        "fragment_index": 1,
        "text_description": "Arc Length \\(L = r\\theta\\)",
        "image_description": ""
      },
      {
        "fragment_index": 2,
        "text_description": "Dynamic exploration: adjust the radius and angle sliders and see the sector morph instantly.\nRatio reasoning: confirm the live value follows \\(L = r\\theta\\) (θ in radians).\nChallenge: fine-tune r and θ until the displayed arc length hits 10 cm ± 0.1 cm.\nAchieve the goal and the simulation will cheer: “Perfect! Your selections produce a 10 cm arc.”",
        "image_description": ""
      }
    ]
  },
  {
    "slide": 9,
    "fragments": [
      {
        "fragment_index": -1,
        "text_description": "Multiple Choice Question\nSubmit Answer\n// MCQ interaction logic\n        const correctOption = 2; // 0-based index for \\(\\dfrac{7\\pi}{3}\\) cm\n        const answerCards = document.querySelectorAll('.answer-card');\n        const submitBtn = document.getElementById('slide-10-x9b3kq-submitBtn');\n        const feedbackCorrect = document.getElementById('slide-10-x9b3kq-feedback-correct');\n        const feedbackIncorrect = document.getElementById('slide-10-x9b3kq-feedback-incorrect');\n        \n        let selectedOption = null;\n        \n        answerCards.forEach((card, index) => {\n            card.addEventListener('click', () => {\n                answerCards.forEach(c => c.classList.remove('border-blue-500','bg-blue-50'));\n                card.classList.add('border-blue-500','bg-blue-50');\n                selectedOption = index;\n            });\n        });\n        \n        submitBtn.addEventListener('click', () => {\n            if (selectedOption === null) return;\n            if (selectedOption === correctOption) {\n                feedbackCorrect.classList.remove('hidden');\n                feedbackIncorrect.classList.add('hidden');\n            } else {\n                feedbackIncorrect.classList.remove('hidden');\n                feedbackCorrect.classList.add('hidden');\n            }\n        });",
        "image_description": ""
      },
      {
        "fragment_index": 1,
        "text_description": "Question\nIn a circle of radius 7 cm, what is the length of the arc that subtends a 60° angle at the centre? (Use \\(\\pi\\) as needed.)",
        "image_description": ""
      },
      {
        "fragment_index": 2,
        "text_description": "1\n\\(7\\pi\\) cm",
        "image_description": ""
      },
      {
        "fragment_index": 3,
        "text_description": "2\n\\(14\\pi\\) cm",
        "image_description": ""
      },
      {
        "fragment_index": 4,
        "text_description": "3\n\\(\\dfrac{7\\pi}{3}\\) cm",
        "image_description": ""
      },
      {
        "fragment_index": 5,
        "text_description": "4\n\\(\\dfrac{7\\pi}{6}\\) cm",
        "image_description": ""
      },
      {
        "fragment_index": 6,
        "text_description": "Hint:\nUse \\(l=\\frac{\\theta}{360^{\\circ}}\\times2\\pi r\\).",
        "image_description": ""
      },
      {
        "fragment_index": 7,
        "text_description": "Correct!\nGreat job! You applied the arc-length formula correctly.",
        "image_description": ""
      },
      {
        "fragment_index": 8,
        "text_description": "Incorrect\nRemember: divide the angle by \\(360^{\\circ}\\) and multiply by \\(2\\pi r\\).",
        "image_description": ""
      }
    ]
  },
  {
    "slide": 10,
    "fragments": [
      {
        "fragment_index": -1,
        "text_description": "Circle Key Takeaways",
        "image_description": ""
      },
      {
        "fragment_index": 1,
        "text_description": "Recap: Angles & Arcs\nCentral angle is twice the inscribed angle on the same arc.",
        "image_description": ""
      },
      {
        "fragment_index": 2,
        "text_description": "Recap: Tangent Rule\nA radius meets its tangent at 90°. Use this for distance proofs.",
        "image_description": ""
      },
      {
        "fragment_index": 3,
        "text_description": "Next Steps: Practice\nSolve Exercise 10.2 to consolidate every circle fact you learned.",
        "image_description": ""
      },
      {
        "fragment_index": 4,
        "text_description": "Next Steps: Explore Further\nPreview cyclic quadrilaterals; note opposite angles add to \\(180^{\\circ}\\).",
        "image_description": ""
      }
    ]
  }
]