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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 that lie at a fixed distance, called the radius, from a fixed point, called the centre.",
"image_description": ""
},
{
"fragment_index": 4,
"text_description": "centre → fixed point | radius → common distance",
"image_description": ""
}
]
},
{
"slide": 2,
"fragments": [
{
"fragment_index": -1,
"text_description": "Chord vs Arc",
"image_description": ""
},
{
"fragment_index": 1,
"text_description": "Chord (straight) and Arc (curved) joining the same endpoints",
"image_description": "https://asset.sparkl.ac/pb/sparkl-vector-images/img_ncert/owrleLmAGshxwGTx6VoTGBpVdgGQgY7PSWc4F5Tw.png"
},
{
"fragment_index": 2,
"text_description": "Spot the difference\nA chord is a straight line segment joining two points on a circle.\nAn arc is the curved part of the circle’s circumference between the same two points.\nKey Points:\nChord lies inside the circle; arc lies on the circumference.\nChord length is a straight distance; arc length follows the curve.\nEach chord defines two arcs: a minor arc (< 180°) and a major arc (> 180°).",
"image_description": ""
}
]
},
{
"slide": 3,
"fragments": [
{
"fragment_index": -1,
"text_description": "Measuring Arc Length",
"image_description": ""
},
{
"fragment_index": 1,
"text_description": "\\[s = r\\,\\theta\\]",
"image_description": ""
},
{
"fragment_index": 2,
"text_description": "Variable Definitions",
"image_description": ""
},
{
"fragment_index": 3,
"text_description": "\\(s\\)\nArc length (same unit as \\(r\\))",
"image_description": ""
},
{
"fragment_index": 4,
"text_description": "\\(r\\)\nRadius of circle",
"image_description": ""
},
{
"fragment_index": 5,
"text_description": "\\( \\theta \\)\nCentral angle (radians)",
"image_description": ""
},
{
"fragment_index": 6,
"text_description": "Applications",
"image_description": ""
},
{
"fragment_index": 7,
"text_description": "Angle vs Length\nBigger \\( \\theta \\) means a longer arc—think of cutting a larger pizza slice.",
"image_description": ""
},
{
"fragment_index": 8,
"text_description": "Wheel Distance\nA wheel rolls distance \\(s\\) when it spins through \\( \\theta \\) radians with radius \\(r\\).",
"image_description": ""
}
]
},
{
"slide": 4,
"fragments": []
},
{
"slide": 5,
"fragments": [
{
"fragment_index": -1,
"text_description": "Sector of a Circle",
"image_description": ""
},
{
"fragment_index": 1,
"text_description": "Highlighted minor sector of a circle",
"image_description": "https://asset.sparkl.ac/pb/sparkl-vector-images/img_ncert/0d6nAfX2XdnO6X1LYTLTeTfXYPnHz6RkMpSZQss9.png"
},
{
"fragment_index": 2,
"text_description": "Definition & Everyday Picture\nA sector is the region bounded by two radii and the arc between them.\nThink of a pizza slice or the sweep of a speedometer needle.\nKey Points:\nMinor sector: angle < \\(180^\\circ\\) — smaller part of the circle.\nMajor sector: angle > \\(180^\\circ\\) — larger complementary part.\nFraction relation: major sector = \\(1 -\\) (minor sector fraction).",
"image_description": ""
}
]
},
{
"slide": 6,
"fragments": [
{
"fragment_index": -1,
"text_description": "Angle at Centre Rule",
"image_description": ""
},
{
"fragment_index": 1,
"text_description": "",
"image_description": "https://asset.sparkl.ac/pb/sparkl-vector-images/img_ncert/XkmG6IIgToMNs0HJ7fDgO2y4Ln78OBUYqDyv1eTI.png"
},
{
"fragment_index": 2,
"text_description": "Key Theorem\nFor a given arc, the angle at the centre is always twice the angle at the circumference on that arc.\nExample: if the circumference angle is \\(30^{\\circ}\\), predict the central angle, then enter it in the quiz.",
"image_description": ""
},
{
"fragment_index": 3,
"text_description": "Key Points:\nCentral angle \\(= 2 \\times\\) circumference angle.\nNotation: \\( \\angle AOB = 2\\,\\angle ACB \\) on arc \\(AB\\).\nRatio 2 : 1 holds for every arc of a circle.",
"image_description": ""
}
]
},
{
"slide": 7,
"fragments": [
{
"fragment_index": -1,
"text_description": "Key Takeaways",
"image_description": ""
},
{
"fragment_index": 1,
"text_description": "Circle = Locus of Points\nRevision: all points \\(r\\) units from a fixed centre form a circle.",
"image_description": ""
},
{
"fragment_index": 2,
"text_description": "Chord, Arc & Sector\nRevision: a chord is a straight cut, its curve is an arc, both bound a sector.",
"image_description": ""
},
{
"fragment_index": 3,
"text_description": "Arc Length & Central-Angle\nKey idea: \\( \\frac{L}{2\\pi r} = \\frac{\\theta}{360^\\circ} \\) links length to angle.",
"image_description": ""
},
{
"fragment_index": 4,
"text_description": "Next Steps\nApply these basics to tangents, cyclic quadrilaterals and angle properties next.",
"image_description": ""
}
]
}
]