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angle bisector wanted, two tangents given

Source: North Macedonian Mathematical Olympiad 1999 p3

February 12, 2020

geometryangle bisectorTangents

Problem Statement

Let the two tangents from a point

A

outside a circle

k

touch

k

M

and

N

. A line

p

through

A

intersects

k

B

and

C

, and

D

is the midpoint of

MN

. Prove that

MN

bisects the angle

BDC