MathDB

A classical geometry problem

Source: Bundeswettbewerb Mathematik 2021, Round 2 - Problem 3

September 22, 2021

geometrygeometry proposedtangentangle bisector

Problem Statement

We are given a circle

k

and a point

A

outside of

k

. Next we draw three lines through

A

: one secant intersecting the circle

k

at points

B

and

C

, and two tangents touching the circle

k

at points

D

and

E

. Let

F

be the midpoint of

DE

.
Show that the line

DE

bisects the angle

\angle BFC