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Mediterranean Mathematics Olympiad
2003 Mediterranean Mathematics Olympiad
2
2
Part of
2003 Mediterranean Mathematics Olympiad
Problems
(1)
Prove that CAP = 2 CPA
Source: Mediterranean MO 2003
10/31/2010
In a triangle
A
B
C
ABC
A
BC
with
B
C
=
C
A
+
1
2
A
B
BC = CA + \frac 12 AB
BC
=
C
A
+
2
1
A
B
, point
P
P
P
is given on side
A
B
AB
A
B
such that
B
P
:
P
A
=
1
:
3
BP : PA = 1 : 3
BP
:
P
A
=
1
:
3
. Prove that
∠
C
A
P
=
2
∠
C
P
A
.
\angle CAP = 2 \angle CPA.
∠
C
A
P
=
2∠
CP
A
.
trigonometry
calculus
derivative
conics
hyperbola
geometry unsolved
geometry