MathDB

A lot of circle

Source: Pan African 2001

October 4, 2005

quadraticsgeometryperpendicular bisectoralgebra

Problem Statement

Let

S_1

be a semicircle with centre

O

and diameter

AB

.A circle

C_1

with centre

P

is drawn, tangent to

S_1

, and tangent to

AB

at

O

. A semicircle

S_2

is drawn, with centre

Q

on

AB

, tangent to

S_1

and to

C_1

. A circle

C_2

with centre

R

is drawn, internally tangent to

S_1

and externally tangent to

S_2

and

C_1

. Prove that

OPRQ

is a rectangle.

Back to Problems View on AoPS