MathDB

The right triangles

ABC

and

AB_1C_1

are similar and have opposite orientation. The right angles are at

C

and

C_1

, and we also have

\angle CAB = \angle C_1AB_1

. Let

M

be the point of intersection of the lines

BC_1

and

B_1C

. Prove that if the lines

AM

and

CC_1

exist, they are perpendicular.

Problem Statement