MathDB
Problems
Contests
National and Regional Contests
Slovenia Contests
Slovenia Team Selection Tests
1998 Slovenia Team Selection Test
2
2
Part of
1998 Slovenia Team Selection Test
Problems
(1)
perpendicular wanted starting with a semicircle
Source: Slovenia TST 1998 p2
2/15/2020
A semicircle with center
O
O
O
and diameter
A
B
AB
A
B
is given. Point
M
M
M
on the extension of
A
B
AB
A
B
is taken so that
A
M
>
B
M
AM > BM
A
M
>
BM
. A line through
M
M
M
intersects the semicircle at
C
C
C
and
D
D
D
so that
C
M
<
D
M
CM < DM
CM
<
D
M
. The circumcircles of triangles
A
O
D
AOD
A
O
D
and
O
B
C
OBC
OBC
meet again at point
K
K
K
. Prove that
O
K
OK
O
K
and
K
M
KM
K
M
are perpendicular
perpendicular
semicircle