MathDB

PAMO 2016 Q1

Source: PAMO 2016

April 29, 2016

geometrycommon tangents

Problem Statement

Two circles

\mathcal{C}_1

and

\mathcal{C}_2

intersect each other at two distinct points

M

and

N

. A common tangent lines touches

\mathcal{C}_1

at

P

and

\mathcal{C}_2

at

Q

, the line being closer to

N

than to

M

. The line

PN

meets the circle

\mathcal{C}_2

again at the point

R

. Prove that the line

MQ

is a bisector of the angle

\angle{PMR}

.

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