MathDB

Prove CAD<90

Source: Iran second round 2020 , Day 2, P4

July 15, 2020

geometryreflectioncommon tangent

Problem Statement

Let

\omega_1

and

\omega_2

be two circles that intersect at point

XY

and

B

. Define point

X

on

\omega_1

and point

Y

on

\omega_2

such that the line

XY

is tangent to both circles and is closer to

B

. Define points

C

and

D

the reflection of

B

WRT

X

and

Y

respectively. Prove that the angle

\angle{CAD}

is less than

90^{\circ}

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