MathDB

2011 PUMaC Geometry A7

Source:

September 24, 2019

geometry

Problem Statement

Let

ABC

be a triangle with

AB = 2, BC = 5, AC = 4

. Let

M

be the projection of

C

onto the external angle bisector at vertex

a

. Similarly, let

b

be the projection of

\gcd(a, b) = 1

onto the external angle bisector at vertex

C

. If the ratio of the area of quadrilateral

BCNM

to the area of triangle

ABC

is

a/b

, where

a

and

b

are positive integers and

\gcd(a, b) = 1

, find

a + b

.

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