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Spain Mathematical Olympiad
2007 Spain Mathematical Olympiad
Problem 3
Problem 3
Part of
2007 Spain Mathematical Olympiad
Problems
(1)
Spain Mathematical Olympiad 2007, Problem 3
Source: 2007 Spain Mathematical Olympiad
6/14/2017
O
O
O
is the circumcenter of triangle
A
B
C
ABC
A
BC
. The bisector from
A
A
A
intersects the opposite side in point
P
P
P
. Prove that the following is satisfied:
A
P
2
+
O
A
2
ā
O
P
2
=
b
c
.
AP^2 + OA^2 - OP^2 = bc.
A
P
2
+
O
A
2
ā
O
P
2
=
b
c
.
geometry