MathDB

3 circles, 1 centered in the intersection of the 2 others

Source: JBMO Shortlist 2004

October 13, 2017

JBMOgeometry

Problem Statement

Two circles

C_1

and

C_2

intersect in points

A

and

B

. A circle

C

with center in

A

intersect

C_1

in

M

and

P

and

C_2

in

N

and

Q

so that

N

and

Q

are located on different sides wrt

MP

and

AB> AM

. Prove that

\angle MBQ = \angle NBP

.

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