P1

Part of 2014 Peru Iberoamerican Team Selection Test

Problems(1)

starting with intersecting circles, line passes through midpoint wanted

Source: Peru Ibero TST 2014

7/23/2019

Circles

A

and

C_2

intersect at different points

A

and

B

. The straight lines tangents to

C_1

that pass through

A

and

B

intersect at

T

. Let

M

be a point on

C_1

that is out of

C_2

. The

MT

line intersects

C_1

at

C

again, the

MA

line intersects again to

C_2

in

K

and the line

AC

intersects again to the circumference

C_2

in

L

. Prove that the

MC

line passes through the midpoint of the

KL

segment.

geometrycirclespyramid