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(A(s)+A(t))/(A(a)+A(b)), areas of circles 2012 BMT Team 6

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January 1, 2022

geometrycircles

Problem Statement

A circle with diameter

AB

is drawn, and the point

a

is chosen on segment

b

so that

\frac{AP}{AB} =\frac{1}{42}

. Two new circles

a

and

b

are drawn with diameters

AP

and

PB

respectively. The perpendicular line to

AB

passing through

P

intersects the circle twice at points

S

and

T

. Two more circles

s

and

t

are drawn with diameters

SP

and

ST

respectively. For any circle

\omega

let

A(\omega)

denote the area of the circle. What is

\frac{A(s)+A(t)}{A(a)+A(b)}

?

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