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International Contests
International Olympiad of Metropolises
2020 IOM
1
1
Part of
2020 IOM
Problems
(1)
Prove that $CK=ML$
Source: Metropolises 2020 P1
12/18/2020
In a triangle
A
B
C
ABC
A
BC
with a right angle at
C
C
C
, the angle bisector
A
L
AL
A
L
(where
L
L
L
is on segment
B
C
BC
BC
) intersects the altitude
C
H
CH
C
H
at point
K
K
K
. The bisector of angle
B
C
H
BCH
BC
H
intersects segment
A
B
AB
A
B
at point
M
M
M
. Prove that
C
K
=
M
L
CK=ML
C
K
=
M
L
geometry
angle bisector