Transcript: Circles_20250701_055430.html

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[
  {
    "slide": 1,
    "fragments": [
      {
        "fragment_index": -1,
        "text_description": "What Is a Circle?",
        "image_description": ""
      },
      {
        "fragment_index": 1,
        "text_description": "Circle",
        "image_description": ""
      },
      {
        "fragment_index": 2,
        "text_description": "A circle is the collection of all points that are the same distance, called the radius, from a fixed centre.",
        "image_description": ""
      }
    ]
  },
  {
    "slide": 2,
    "fragments": [
      {
        "fragment_index": -1,
        "text_description": "Arc vs Chord",
        "image_description": ""
      },
      {
        "fragment_index": 1,
        "text_description": "Identify the highlighted arc (curved) and chord (straight).",
        "image_description": "https://sparkl-vector-images.s3.ap-south-1.amazonaws.com/presentation_images/asset.sparkl.me/pb/presentation/2558/images/c28393a344f1aca89c22af0301c0dfb3.png"
      },
      {
        "fragment_index": 2,
        "text_description": "Parts of a Circle\nToday we focus on two parts of a circle.\nLearn to tell an arc from a chord in any diagram.",
        "image_description": ""
      },
      {
        "fragment_index": 3,
        "text_description": "Key Points:\nArc – curved portion of the circumference.\nChord – straight line linking two points on the circle.",
        "image_description": ""
      }
    ]
  },
  {
    "slide": 3,
    "fragments": [
      {
        "fragment_index": -1,
        "text_description": "Multiple Choice Question\nSubmit Answer\nCorrect!\nGood job! Radius = diameter ÷ 2 → 10 ÷ 2 = 5 cm.\nIncorrect\nRemember: the radius is half the diameter, so 10 cm ÷ 2 = 5 cm.\nconst correctOption = 0;\n        const answerCards = document.querySelectorAll('.answer-card');\n        const submitBtn = document.getElementById('submitBtn');\n        const feedbackCorrect = document.getElementById('feedbackCorrect');\n        const feedbackIncorrect = document.getElementById('feedbackIncorrect');\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\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": 0,
        "text_description": "Question\nThe diameter of a circle is 10 cm. Find its radius.",
        "image_description": ""
      },
      {
        "fragment_index": 1,
        "text_description": "A\n5 cm",
        "image_description": ""
      },
      {
        "fragment_index": 2,
        "text_description": "B\n10 cm",
        "image_description": ""
      },
      {
        "fragment_index": 3,
        "text_description": "C\n15 cm",
        "image_description": ""
      },
      {
        "fragment_index": 4,
        "text_description": "D\n20 cm",
        "image_description": ""
      },
      {
        "fragment_index": 5,
        "text_description": "Hint:\nDivide the diameter by 2 to get the radius.",
        "image_description": ""
      }
    ]
  },
  {
    "slide": 4,
    "fragments": [
      {
        "fragment_index": -1,
        "text_description": "Formula for Arc Length",
        "image_description": ""
      },
      {
        "fragment_index": 1,
        "text_description": "Arc highlighted by central angle θ",
        "image_description": "https://sparkl-vector-images.s3.ap-south-1.amazonaws.com/img/lp/study_content/lp/1/11/4/182/651/1249/1237/21-5-09_LP_Vandana_Phy_1.11.4.4.2.4_srav_SS_html_m162ce79c.png"
      },
      {
        "fragment_index": 2,
        "text_description": "Arc Length Formula\nArc length is the distance along a circle's curved edge.\nUse the formula below to write or identify the length of any arc.\nKey Points:\n\\(L = 2\\pi r \\times \\dfrac{\\theta}{360^\\circ}\\)\n\\(r\\) — radius of the circle\n\\( \\theta \\) — central angle in degrees\nSubstitute values to compute or verify arc length.",
        "image_description": ""
      }
    ]
  },
  {
    "slide": 5,
    "fragments": [
      {
        "fragment_index": -1,
        "text_description": "Worked Example\nGoal: Calculate the length of a \\(60^\\circ\\) arc on a 7 cm circle.",
        "image_description": ""
      },
      {
        "fragment_index": 1,
        "text_description": "1\nNote radius and angle\nRadius \\(r = 7\\,\\text{cm}\\); central angle \\(\\theta = 60^\\circ\\).",
        "image_description": ""
      },
      {
        "fragment_index": 2,
        "text_description": "2\nWrite arc formula\n\\(L = 2\\pi r \\times \\frac{\\theta}{360^\\circ}\\).",
        "image_description": ""
      },
      {
        "fragment_index": 3,
        "text_description": "3\nSubstitute values\n\\(L = 2\\pi(7)\\times\\frac{60}{360}\\).",
        "image_description": ""
      },
      {
        "fragment_index": 4,
        "text_description": "4\nSimplify & calculate\n\\(\\frac{60}{360} = \\frac16\\); \\(L = 14\\pi \\times \\frac16 = \\frac{14\\pi}{6} \\approx 7.33\\,\\text{cm}\\).",
        "image_description": ""
      },
      {
        "fragment_index": 5,
        "text_description": "Pro Tip:\nKeep \\(\\theta\\) in degrees when using this version of the arc length formula.",
        "image_description": ""
      }
    ]
  },
  {
    "slide": 6,
    "fragments": [
      {
        "fragment_index": -1,
        "text_description": "Angle at Centre Rule",
        "image_description": ""
      },
      {
        "fragment_index": 1,
        "text_description": "Central angle \\(2x\\) is twice circumference angle \\(x\\).",
        "image_description": "https://sparkl-vector-images.s3.ap-south-1.amazonaws.com/img/lp/study_content/lp/100/100/1/3150/8190/29361/Chap-10_Lesson-8_m.6.6.10_MAN_CHT_Lang.edited_html_468205b8.png"
      },
      {
        "fragment_index": 2,
        "text_description": "Angle at Centre Theorem\nIn a circle, the angle at the centre is twice the angle at the circumference made by the same chord.\nKey Points:\n\\( \\angle\\text{centre} = 2 \\times \\angle\\text{circumference} \\)\nBoth angles subtend the same chord.\nApplies to minor and major arcs alike.",
        "image_description": ""
      }
    ]
  },
  {
    "slide": 7,
    "fragments": [
      {
        "fragment_index": -1,
        "text_description": "Multiple Choice Question\nSubmit Answer\nCorrect!\nWell done! 50° is half of 100°, applying the angle at centre theorem.\nIncorrect\nCheck the theorem: circumference angle = half the central angle. Try again.\nconst correctOption = 1;\n        const answerCards = document.querySelectorAll('.answer-card');\n        const submitBtn = document.getElementById('submitBtn');\n        const feedbackCorrect = document.getElementById('feedbackCorrect');\n        const feedbackIncorrect = document.getElementById('feedbackIncorrect');\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            \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\nThe angle at the centre of a circle is 100°. What is the corresponding angle at the circumference?",
        "image_description": ""
      },
      {
        "fragment_index": 2,
        "text_description": "1\n25°",
        "image_description": ""
      },
      {
        "fragment_index": 3,
        "text_description": "2\n50°",
        "image_description": ""
      },
      {
        "fragment_index": 4,
        "text_description": "3\n100°",
        "image_description": ""
      },
      {
        "fragment_index": 5,
        "text_description": "4\n200°",
        "image_description": ""
      },
      {
        "fragment_index": 6,
        "text_description": "Hint:\nAngle at circumference = ½ × central angle.",
        "image_description": ""
      }
    ]
  },
  {
    "slide": 8,
    "fragments": [
      {
        "fragment_index": -1,
        "text_description": "Tangent Facts\nKey Tangent Rules\nRecall these two key tangent properties to solve circle problems.",
        "image_description": ""
      },
      {
        "fragment_index": 1,
        "text_description": "",
        "image_description": "https://sparkl-vector-images.s3.ap-south-1.amazonaws.com/presentation_images/asset.sparkl.me/pb/presentation/2558/images/c28393a344f1aca89c22af0301c0dfb3.png"
      },
      {
        "fragment_index": 2,
        "text_description": "Key Points:\nTangent & Radius: They meet at \\(90^{\\circ}\\).\nEqual Tangents: From the same external point, their lengths are equal.",
        "image_description": ""
      }
    ]
  },
  {
    "slide": 9,
    "fragments": [
      {
        "fragment_index": -1,
        "text_description": "Circle Key Ideas\nThank You!\nRecap complete—you can now state every key idea with confidence.",
        "image_description": ""
      },
      {
        "fragment_index": 1,
        "text_description": "Centre, radius and diameter define a circle.",
        "image_description": ""
      },
      {
        "fragment_index": 2,
        "text_description": "Chord joins two points; arc is curved path between them.",
        "image_description": ""
      },
      {
        "fragment_index": 3,
        "text_description": "Arc length: \\(L = 2\\pi r \\times \\frac{\\theta}{360^\\circ}\\).",
        "image_description": ""
      },
      {
        "fragment_index": 4,
        "text_description": "Angle at centre equals twice angle at circumference.",
        "image_description": ""
      },
      {
        "fragment_index": 5,
        "text_description": "Tangent meets circle once, ⟂ radius; equal tangents from one point.",
        "image_description": ""
      }
    ]
  }
]