geometry problems from Cyberspace Mathematical Competition (CMC)
with aops links in the names
2020
Let ABC be a triangle such that AB > BC and let D be a variable point on the line segment BC. Let E be the point on the circumcircle of triangle ABC, lying on the opposite side of BC from A such that \angle BAE = \angle DAC. Let I be the incenter of triangle ABD and let J be the incenter of triangle ACE. Prove that the line IJ passes through a fixed point, that is independent of D.
Find all integers n\geq 3 for which the following statement is true: If \mathcal{P} is a convex n-gon such that n-1 of its sides have equal length and n-1 of its angles have equal measure, then \mathcal{P} is a regular polygon. (A regular polygon is a polygon with all sides of equal length, and all angles of equal measure.)
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