MathDB

2022 Geometry 6

Source:

March 14, 2022

geometry

Problem Statement

Let

ABCD

be a rectangle inscribed in circle

\Gamma

, and let

P

be a point on minor arc

AB

of

\Gamma

. Suppose that

P A \cdot P B = 2

,

P C \cdot P D = 18

, and

P B \cdot P C = 9

. The area of rectangle

ABCD

can be expressed as

\frac{a\sqrt{b}}{c}

, where

a

and

c

are relatively prime positive integers and

b

is a squarefree positive integer. Compute

100a + 10b + c

.

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