MathDB

Given is a triangle

ABC

and a point

K

within the triangle. The point

K

is mirrored in the sides of the triangle:

P , Q

and

R

are the mirrorings of

K

AB , BC

and

CA

, respectively .

M

is the center of the circle passing through the vertices of triangle

PQR

M

is mirrored again in the sides of triangle

ABC

P', Q'

and

R'

are the mirror of

M

AB

respectively,

BC

and

CA

. a. Prove that

K

is the center of the circle passing through the vertices of triangle

P'Q'R'

. b. Where should you choose

K

within triangle

ABC

so that

M

and

K

coincide? Prove your answer.

Problem Statement