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2022 MMATHS Team Online p12 - 5th and final geo on the test, long live geo

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October 1, 2023

geometryMMATHS

Problem Statement

Let triangle

D

with incenter

I

satisfy

AB = 3

,

AC = 4

, and

E

. Suppose that

D

and

E

lie on

AB

and

AC

, respectively, such that

IP = BP

,

I

, and

E

are collinear and

DE \perp AI

. Points

P

and

Q

lie on side

BC

such that

IP = BP

and

IQ = CQ

, and lines

DP

and

EQ

meet at

S

. Compute

SI^2

.

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