MathDB

Tangent lines and a tangent circle

Source: Korea National Olympiad 2014 #3

November 7, 2014

geometryincenterKorea

Problem Statement

AB

is a chord of

O

and

AB

is not a diameter of

O

. The tangent lines to

C

at

O

and

MN

meet at

C

. Let

M

and

N

be the midpoint of the segments

AC

and

BC

, respectively. A circle passing through

C

and tangent to

O

meets line

MN

at

P

and

Q

. Prove that

\angle PCQ = \angle CAB

.

Back to Problems View on AoPS