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TOT 2004 Spring - Junior A-Level p4 collinear, common tangent

Source:

February 25, 2020

tangentcirclesgeometrycollinear

Problem Statement

Two circles intersect in points

A

and

B

. Their common tangent nearer

B

touches the circles at points

E

and

F

, and intersects the extension of

AB

at the point

M

. The point

K

is chosen on the extention of

AM

so that

KM = MA

. The line

KE

intersects the circle containing

E

again at the point

C

. The line

KF

intersects the circle containing

F

again at the point

D

. Prove that the points

A, C

and

D

are collinear.

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