MathDB

Poland 2017 P1

Source:

April 4, 2017

geometrycircumcirclegeometry solvedMiquel pointSpiral SimilarityAngle Chasingcyclic quadrilateral

Problem Statement

Points

P

and

Q

lie respectively on sides

AB

and

AC

of a triangle

ABC

and

BP=CQ

. Segments

BAC

and

CP

cross at

R

. Circumscribed circles of triangles

BPR

and

CQR

cross again at point

S

different from

R

. Prove that point

S

lies on the bisector of angle

BAC

.

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