MathDB

2015-2016 Spring OMO #14

Source:

March 29, 2016

Online Math Open

Problem Statement

Let

ABC

be a triangle with

BC=20

and

CA=16

, and let

I

be its incenter. If the altitude from

A

to

BC

, the perpendicular bisector of

AC

, and the line through

I

perpendicular to

AB

intersect at a common point, then the length

AB

can be written as

m+\sqrt{n}

for positive integers

m

and

n

. What is

100m+n

?
Proposed by Tristan Shin

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