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BR = 2XY wanted, AR = BP, AQ = AB ,tangent to circumcircle related

Source: Switzerland - Swiss ΜΟ 2017 p5

July 14, 2020

geometrycircumcircleequal segmentstangent

Problem Statement

Let

ABC

be a triangle with

AC> AB

. Let

P

be the intersection of

BC

and the tangent through

A

around the triangle

ABC

. Let

Q

be the point on the straight line

AC

, so that

AQ = AB

and

A

is between

C

and

Q

. Let

X

and

Y

be the center of

BQ

and

AP

. Let

R

be the point on

AP

so that

AR = BP

and

R

is between

A

and

P

. Show that

BR = 2XY

.

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