MathDB

Squares in Circles

Source:

December 28, 2006

ratiogeometrynumber theoryrelatively primePythagorean Theorempower of a point

Problem Statement

Square

ABCD

is inscribed in a circle. Square

EFGH

has vertices

E

and

F

on

\overline{CD}

and vertices

G

and

H

on the circle. The ratio of the area of square

EFGH

to the area of square

ABCD

can be expressed as

\frac{m}{n}

where

m

and

n

are relatively prime positive integers and

m<n

. Find

10n+m

.

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