MathDB
Problems
Contests
National and Regional Contests
Bosnia Herzegovina Contests
Bosnia Herzegovina Team Selection Test
2012 Bosnia Herzegovina Team Selection Test
1
Bosnia and Herzegovina TST 2012 Problem 1
Bosnia and Herzegovina TST 2012 Problem 1
Source:
May 19, 2012
geometry
circumcircle
geometry proposed
Problem Statement
Let
D
D
D
be the midpoint of the arc
B
−
A
−
C
B-A-C
B
−
A
−
C
of the circumcircle of
△
A
B
C
(
A
B
<
A
C
)
\triangle ABC (AB<AC)
△
A
BC
(
A
B
<
A
C
)
. Let
E
E
E
be the foot of perpendicular from
D
D
D
to
A
C
AC
A
C
. Prove that
∣
C
E
∣
=
∣
B
A
∣
+
∣
A
C
∣
2
|CE|=\frac{|BA|+|AC|}{2}
∣
CE
∣
=
2
∣
B
A
∣
+
∣
A
C
∣
.
Back to Problems
View on AoPS