MathDB

2021 Geo Div 1 P8

Source:

March 2, 2021

geometry

Problem Statement

Let

ABC

be a triangle with

AB < AC

and

\omega

be a circle through

A

tangent to both the

AB, AC

-excircle and the

C

-excircle. Let

\omega

intersect lines

AB, AC

at

X,Y

respectively and

X,Y

lie outside of segments

AB, AC

. Let

O

be the center of

\omega

and let

OI_C, OI_B

intersect line

BC

at

J,K

respectively. Suppose

KJ = 4

,

KO = 16

and

OJ = 13

. Find

\frac{[KI_BI_C]}{[JI_BI_C]}

.
Proposed by Grant Yu

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