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P29 [Geometry] - Turkish NMO 1st Round - 2014

Source:

May 26, 2014

geometryanalytic geometrytrapezoidangle bisector

Problem Statement

Let

ABC

be a triangle such that

|AB|=13 , |BC|=12

and

|CA|=5

. Let the angle bisectors of

A

and

B

intersect at

I

and meet the opposing sides at

D

and

E

, respectively. The line passing through

I

and the midpoint of

[DE]

meets

[AB]

at

F

. What is

|AF|

?

<span class='latex-bold'>(A)</span>\ \dfrac{3}{2} \qquad<span class='latex-bold'>(B)</span>\ 2 \qquad<span class='latex-bold'>(C)</span>\ \dfrac{5}{2} \qquad<span class='latex-bold'>(D)</span>\ 3 \qquad<span class='latex-bold'>(E)</span>\ \dfrac{7}{2}

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