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Czech Republic Contests
District Round (Round II)
2008 District Round (Round II)
4
4
Part of
2008 District Round (Round II)
Problems
(1)
Czech republic,district round,2008,problem 4
Source:
2/25/2012
A semicircle has diameter
A
B
AB
A
B
and center
S
S
S
,with a point
M
M
M
on the circumference.
U
,
V
U,V
U
,
V
are the incircles of sectors
A
S
M
ASM
A
SM
and
B
S
M
BSM
BSM
.Prove that circles
U
,
V
U,V
U
,
V
can be seperated by a line perpendicular to
A
B
AB
A
B
.
geometry
calculus
function
geometry proposed