MathDB

Lots of circles

Source: Science ON 2021 Seniors/4

March 14, 2021

geometryAngle ChasingcirclesProjective

Problem Statement

ABCD

is a cyclic convex quadrilateral whose diagonals meet at

X

. The circle

(AXD)

cuts

CD

again at

V

and the circle

(BXC)

cuts

AB

again at

U

, such that

D

lies strictly between

C

and

V

and

B

lies strictly between

A

and

T

. Let

(UPV)

.\\ \\ If

M

is the intersection point of the tangents to

\angle PTM=90^o

and

V

at

(UPV)

and

T

is the second intersection of circles

(UPV)

and

(PAC)

, prove that

\angle PTM=90^o

.\\ \\ (Vlad Robu)

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