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[
{
"slide": 1,
"fragments": [
{
"fragment_index": -1,
"text_description": "Circles Kickoff\nEqual distance, perfect shape.",
"image_description": ""
}
]
},
{
"slide": 2,
"fragments": [
{
"fragment_index": -1,
"text_description": "Arc & Chord",
"image_description": ""
},
{
"fragment_index": 1,
"text_description": "",
"image_description": ""
},
{
"fragment_index": 2,
"text_description": "Spot the Difference",
"image_description": ""
},
{
"fragment_index": 3,
"text_description": "Arc AB is the curved part of the circle between points A and B. Chord AB is the straight line segment joining the same two points.",
"image_description": ""
},
{
"fragment_index": 4,
"text_description": "Key Points:\nCurved outline = Arc\nStraight segment = Chord\nArc is usually longer than its chord",
"image_description": ""
}
]
},
{
"slide": 3,
"fragments": [
{
"fragment_index": 1,
"text_description": "Arc Length",
"image_description": ""
},
{
"fragment_index": 2,
"text_description": "\\[ L = 2\\pi r \\left( \\frac{\\theta}{360} \\right) \\]\nUse when \\( \\theta \\) is measured in degrees.",
"image_description": ""
},
{
"fragment_index": 3,
"text_description": "Variable Definitions\nL\narc length\nr\nradius of the circle\nθ\ncentral angle (degrees)",
"image_description": ""
},
{
"fragment_index": 4,
"text_description": "Applications\nMeasuring road bends\nEngineers find curved road length to set safe speed limits.\nDesigning curved rail tracks\nDetermines rail length needed for a smooth train turn.",
"image_description": ""
}
]
},
{
"slide": 4,
"fragments": []
},
{
"slide": 5,
"fragments": [
{
"fragment_index": -1,
"text_description": "Circle Essentials\nThank You!\nGreat job! You can now recall circle terms and the arc length formula.",
"image_description": ""
},
{
"fragment_index": 1,
"text_description": "A circle: all points the same distance from the centre.",
"image_description": ""
},
{
"fragment_index": 2,
"text_description": "Arc: a portion of the circle’s boundary.",
"image_description": ""
},
{
"fragment_index": 3,
"text_description": "Chord: straight line joining any two points on the circle.",
"image_description": ""
},
{
"fragment_index": 4,
"text_description": "Arc length formula \\(L = 2\\pi r \\times \\frac{\\theta}{360^\\circ}\\).",
"image_description": ""
},
{
"fragment_index": 5,
"text_description": "Arc length grows proportionally with radius \\(r\\) or angle \\(\\theta\\).",
"image_description": ""
},
{
"fragment_index": 6,
"text_description": "Next Steps\nTry solving two practice problems on arc length in your workbook.",
"image_description": ""
}
]
}
]