MathDB

perpendicular wanted, intersecting circles and parallel given

Source: Dutch IMO TST1 2015 P4

August 5, 2019

geometryperpendicularparallelcircles

Problem Statement

Let

\Gamma_1

and

\Gamma_2

be circles - with respective centres

O_1

and

O_2

- that intersect each other in

A

and

B

. The line

O_1A

intersects

\Gamma_2

in

A

and

C

and the line

O_2A

intersects

\Gamma_1

in

A

and

D

. The line through

B

parallel to

AD

intersects

\Gamma_1

in

B

and

E

. Suppose that

O_1A

is parallel to

DE

. Show that

CD

is perpendicular to

O_2C

.

Back to Problems View on AoPS