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Angle Bisector in Isosceles Triangle

Source: 2015 AIME I Problem 11

March 20, 2015

geometryangle bisectorAMCAIMEAIME I

Problem Statement

Triangle

ABC

has positive integer side lengths with

AB=AC

. Let

I

be the intersection of the bisectors of

\angle B

and

\angle C

. Suppose

BI=8

. Find the smallest possible perimeter of

\triangle ABC

.

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