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National and Regional Contests
Moldova Contests
JBMO TST - Moldova
2017 Junior Balkan Team Selection Tests - Moldova
Problem 3
Problem 3
Part of
2017 Junior Balkan Team Selection Tests - Moldova
Problems
(1)
Line bisects altitude
Source: Moldova JTST 2017, problem 3
5/3/2017
Let
A
B
C
ABC
A
BC
be a triangle inscribed in a semicircle with center
O
O
O
and diameter
B
C
.
BC.
BC
.
Two tangent lines to the semicircle at
A
A
A
and
B
B
B
intersect at
D
.
D.
D
.
Prove that
D
C
DC
D
C
goes through the midpoint of the altitude
A
H
AH
A
H
of triangle
A
B
C
.
ABC.
A
BC
.
geometry
projective geometry