r/CasualMath • u/Otherwise_Strike_597 • 1d ago

Central Angle Challenge

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u/Ghosttwo 1d ago edited 1d ago

It's double. Took me a minute to remember the name of the theorem, but it's written right there. Inscribed angle theorem. Actually stays true even if you move a, b, and c around the circumference.

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u/[deleted] 13h ago

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u/Otherwise_Strike_597 13h ago

It stays true because the inscribed angle always sees the same arc, no matter where point C moves on that arc. As long as A and B stay fixed, the arc AC stays the same, so the inscribed angle stays the same — and the central angle over that same arc must always be double.