MathDB

2022 Geometry 10

Source:

March 14, 2022

geometry

Problem Statement

Suppose

\omega

is a circle centered at

O

with radius

8

. Let

AC

and

BD

be perpendicular chords of

\omega

. Let

P

be a point inside quadrilateral

ABCD

such that the circumcircles of triangles

ABP

and

CDP

are tangent, and the circumcircles of triangles

ADP

and

BCP

are tangent. If

AC = 2\sqrt{61}

and

BD = 6\sqrt7

,then

OP

can be expressed as

\sqrt{a}-\sqrt{b}

for positive integers

a

and

b

. Compute

100a + b

.

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