MathDB

Geometry with three circles and angular bisectors

Source: Germany 2019, Problem 2

June 20, 2019

geometry

Problem Statement

Let

a

and

b

be two circles, intersecting in two distinct points

Y

and

Z

. A circle

k

touches the circles

a

and

b

externally in the points

A

and

B

.
Show that the angular bisectors of the angles

\angle ZAY

and

\angle YBZ

intersect on the line

YZ