MathDB

Circumcircles tangent

Source: Junior Olympiad of Malaysia Shortlist 2015 G8

July 17, 2015

geometrycircumcircle

Problem Statement

Let

ABCDE

be a convex pentagon such that

BC

and

DE

are tangent to the circumcircle of

ACD

. Prove that if the circumcircles of

ABC

and

ADE

intersect at the midpoint of

CD

, then the circumcircles

ABE

and

ACD

are tangent to each other.