MathDB

Angle bisectors [2011.II.4]

Source:

March 31, 2011

ratiogeometryanalytic geometrygraphing linesslopeAMCAIME

Problem Statement

In triangle

ABC

,

AB=\frac{20}{11} AC

. The angle bisector of

\angle A

intersects

BC

at point

D

, and point

M

is the midpoint of

AD

. Let

P

be the point of the intersection of

AC

and

BM

. The ratio of

CP

to

PA

can be expressed in the form

\dfrac{m}{n}

, where

m

and

n

are relatively prime positive integers. Find

m+n

.

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