MathDB

concurrency, circle tangent ext. to circumcicle and 2 extensions of sides

Source: Balkan MO Shortlist 2008 G5

April 6, 2020

geometrycircumcircleconcurrencyconcurrenttangent circles

Problem Statement

The circle

k_a

touches the extensions of sides

AB

and

BC

, as well as the circumscribed circle of the triangle

ABC

(from the outside). We denote the intersection of

k_a

with the circumscribed circle of the triangle

ABC

A'

. Analogously, we define points

B'

and

C'

. Prove that the lines

AA',BB'

and

CC'

intersect in one point.