MathDB

concurrent wanted, common tangent of intersecting circles related

Source: Switzerland - Swiss MO 2009 p7

July 17, 2020

geometrycommon tangentcirclesconcurrentconcurrency

Problem Statement

Points

A, M_1, M_2

and

C

are on a line in this order. Let

k_1

the circle with center

M_1

passing through

A

and

k_2

the circle with center

M_2

passing through

C

. The two circles intersect at points

E

and

F

. A common tangent of

k_1

and

k_2

, touches

k_1

B

and

k_2

D

. Show that the lines

AB, CD

and

EF

intersect at one point.