Weird geo with two equal circles and centroid
Source: Caucasus MO 2024, Juniors P8
March 15, 2024
geometry
Problem Statement
There are two equal circles of radius placed inside the triangle with side . The circles are tangent to each other, one is inscribed in angle , the other one is inscribed in angle .
(a) Prove that the centroid of the triangle does not lie inside any of the given circles.
(b) Prove that if lies on one of the circles, then the triangle is isosceles.