MathDB
Problems
Contests
National and Regional Contests
Russia Contests
Sharygin Geometry Olympiad
2010 Sharygin Geometry Olympiad
16
16
Part of
2010 Sharygin Geometry Olympiad
Problems
(1)
XC passes through the midpoint of the segment (16)
Source:
10/29/2010
A circle touches the sides of an angle with vertex
A
A
A
at points
B
B
B
and
C
.
C.
C
.
A line passing through
A
A
A
intersects this circle in points
D
D
D
and
E
.
E.
E
.
A chord
B
X
BX
BX
is parallel to
D
E
.
DE.
D
E
.
Prove that
X
C
XC
XC
passes through the midpoint of the segment
D
E
.
DE.
D
E
.
trigonometry
geometry