What happens to the center of the inscribed circle, if one corner of the triangle moves? Of course, the answer depends on the way it moves. Interestingly, the answer is nice, if we move the corner on the circumscribed circle. |
In this construction, I created a track of the center, while C moves. It seems, the center of the inscribed circles moves on circle segments.
Can you prove this. Need a hint? Use the chord angle theorem! Another hint? Computel AMB! It only depends on the angle ACB, which is constant.
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