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Prove that XV=YU (19)

Source:

October 29, 2010

geometryparallelogramcircumcirclegeometry unsolved

Problem Statement

A quadrilateral

ABCD

is inscribed into a circle with center

O.

Points

P

and

Q

are opposite to

C

and

D

respectively. Two tangents drawn to that circle at these points meet the line

AB

in points

E

and

AC

(

BC

is between

E

and

B

,

B

is between

A

and

F

). The line

EO

meets

AC

and

BC

in points

X

and

Y

respectively, and the line

FO

meets

AD

and

BD

in points

U

and

V

respectively. Prove that

XV=YU.

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