MathDB

MMATHS 2021, Problem 10: Olympiad Geometry Medley

Source:

October 31, 2021

YaleMMATHS

Problem Statement

Let

ABC

be a triangle with circumcenter

O

and incenter

I

, and suppose that

OI

meets

AB

and

AC

at

P

and

Q

, respectively. There exists a point

R

on arc

\widehat{BAC}

such that the circumcircles of triangles

PQR

and

ABC

are tangent. Given that

AB = 14

,

BC = 20

, and

CA = 26

, find

\frac{RC}{RB}

.
Proposed by Andrew Wu

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