MathDB

2017 Geometry #10

Source:

November 19, 2022

2017Geometry Test

Problem Statement

Triangle

ABC

is inscribed in circle

\gamma_1

with radius

r_1

. Let

\gamma_2

(with radius

r_2

) be the circle internally tangent to

\gamma_1

at

A

and tangent to

BC

at

D

. Let

I

be the incenter of

P

, and

P

and

Q

be the intersection of

\gamma_2

with

AB

and

AC

respectively. Given that

P

,

I

, and

Q

are collinear,

AI=25

, and the circumradius of triangle

BIC

is

24

, compute the ratio of the radii

\tfrac{r_2}{r_1}

.

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