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National and Regional Contests
Korea Contests
Korea National Olympiad
1996 Korea National Olympiad
4
4
Part of
1996 Korea National Olympiad
Problems
(1)
Circle inside the angle
Source: 1996 Korea National Olympiad #4
3/22/2018
Circle
C
C
C
(the center is
C
C
C
.) is inside the
∠
X
O
Y
\angle XOY
∠
XO
Y
and it is tangent to the two sides of the angle. Let
C
1
C_1
C
1
be the circle that passes through the center of
C
C
C
and tangent to two sides of angle and let
A
A
A
be one of the endpoint of diameter of
C
1
C_1
C
1
that passes through
C
C
C
and
B
B
B
be the intersection of this diameter and circle
C
.
C.
C
.
Prove that the cirlce that
A
A
A
is the center and
A
B
AB
A
B
is the radius is also tangent to the two sides of
∠
X
O
Y
.
\angle XOY.
∠
XO
Y
.
geometry