MathDB

2018 Fall Team #10

Source:

April 17, 2022

geometry

Problem Statement

Let

ABC

be a triangle such that

AB = 13

,

BC = 14

,

AC = 15

. Let

M

be the midpoint of

BC

and define

P \ne B

to be a point on the circumcircle of

ABC

such that

BP \perp PM

. Furthermore, let

H

be the orthocenter of

ABM

and define

Q

to be the intersection of

BP

and

AC

. If

R

is a point on

HQ

such that

RB \perp BC

, find the length of

RB

.

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