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Angle bisectors

Source: 1959 AHSME Problem 28

August 14, 2013

AMCangle bisectorAMC 12geometry

Problem Statement

In triangle

ABC

,

AL

bisects angle

A

and

CM

bisects angle

C

. Points

L

and

M

are on

BC

and

AB

, respectively. The sides of triangle

ABC

are

a,b,

and

c

. Then

\frac{\overline{AM}}{\overline{MB}}=k\frac{\overline{CL}}{\overline{LB}}

where

k

is:

<span class='latex-bold'>(A)</span>\ 1 \qquad<span class='latex-bold'>(B)</span>\ \frac{bc}{a^2}\qquad<span class='latex-bold'>(C)</span>\ \frac{a^2}{bc}\qquad<span class='latex-bold'>(D)</span>\ \frac{c}{b}\qquad<span class='latex-bold'>(E)</span>\ \frac{c}{a}

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