MathDB

MR bisects <AMD, convex ABCD with equal diagonals

Source: III Soros Olympiad 1996-97 R1 10.5 https://artofproblemsolving.com/community/c2416727_soros_olympiad_in_mathematics

May 29, 2024

geometry

Problem Statement

The diagonals of a convex quadrilateral

ABCD

are equal to each other and intersect at point

M

. Points

K

and

L

are taken on

AB

and

CD

, respectively, so that

\frac{AK}{KB}=\frac{DL}{LC}

. Lines

AB

and

KD

intersect at point

P

. Prove that

MP

is the bisector of angle

AMD