IA_2=IB_2=R where A_1, B_1 touchpoints of incircle (I), prove AA_2=BB_2=OI
Source: SRMC 2013
September 2, 2018
geometryincirclecircumcircle
Problem Statement
Circle with center , inscribed in a triangle , touches the sides and at points and respectively. On rays and , respectively, let be the points and such that , where is the radius of the circumscribed circle of the triangle . Prove that:
a) where is the center of the circumscribed circle of the triangle ,
b) lines and intersect on the circumcircle of the triangle .