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Problems
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National and Regional Contests
Czech Republic Contests
District Round (Round II)
2008 District Round (Round II)
2
2
Part of
2008 District Round (Round II)
Problems
(1)
Czech republic,district round,2008,problem 2
Source:
2/25/2012
Two circles
U
,
V
U,V
U
,
V
have distinct radii,tangent to each other externally at
T
T
T
.
A
,
B
A,B
A
,
B
are points on
U
,
V
U,V
U
,
V
respectively,both distinct from
T
T
T
,such that
∠
A
T
B
=
90
\angle ATB=90
∠
A
TB
=
90
. (1)Prove that line
A
B
AB
A
B
passes through a fixed point; (2)Find the locus of the midpoint of
A
B
AB
A
B
.