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Parabola Intersecting Triangle

Source:

August 8, 2024

conicsparabolageometry2022

Problem Statement

Triangle

ABC

has side lengths

AC = 3

,

BC = 4

, and

AB = 5

. Let

I

be the incenter of

\triangle{ABC}

, and let

\mathcal{P}

be the parabola with focus

I

and directrix

\overleftrightarrow{AC}

. Suppose that

\mathcal{P}

intersects

\overline{AB}

and

\overline{BC}

at points

D

and

E

, respectively. Find

DI+EI

.

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