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Both cyclic and circumscribed quadrilateral

Source: Tuymaada 2012, Problem 6, Day 2, Seniors

July 21, 2012

geometryratiotrapezoidtrigonometrytrig identitiesLaw of Sinesgeometry proposed

Problem Statement

Quadrilateral

ABCD

is both cyclic and circumscribed. Its incircle touches its sides

AB

and

CD

at points

X

and

Y

, respectively. The perpendiculars to

AB

and

CD

drawn at

A

and

D

, respectively, meet at point

U

; those drawn at

X

and

Y

meet at point

V

, and finally, those drawn at

B

and

C

meet at point

W

. Prove that points

U

,

V

and

W

are collinear.
Proposed by A. Golovanov

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