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I'm not exactly sure, I wonder if this is consistent. |dw:1446856344730:dw| I made some assumption that when a triangle intersects with a circle on every 3 points, the outer rotation is something 180 deg instead of 360, because i would think that every arc line that seems like it "zoomed out" of the angle is identical in angle. Hope I get corrected if I'm wrong, it's not even in the answers, anyway.
The circle still has 360°. The vertex of the angles in on the circle, so the arcs are twice the measure of the angle.|dw:1446868933696:dw|
Then use the fact that the angles in a triangle add up to 180° to find angle C
Why is it that the angle of the arc corresponding is double that of the pinpointed triangle angle?
proofs http://jwilson.coe.uga.edu/emt668/emat6680.2000/umberger/EMAT6680smu/Assign8smu/inscentproof.html https://www.khanacademy.org/math/geometry/cc-geometry-circles/central-inscribed-circumscribed/v/inscribed-and-central-angles
@peachpi Wow, I didn't try to find the angle that way, that's great! I'll keep this kind of analytical techniques in mind. Thank you!!
You are welcome.