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intersecting equal circles given, arc bisector wanted

Source: Sharygin 2006 finals 8.4

September 10, 2019

bisectsarc midpointarcequal circlesgeometry

Problem Statement

Two equal circles intersect at points

A

and

B

P

is the point of one of the circles that is different from

A

and

B, X

and

Y

are the second intersection points of the lines of

PA, PB

with the other circle. Prove that the line passing through

P

and perpendicular to

AB

divides one of the arcs

XY

in half.