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Paraguay Contests
Paraguay Mathematical Olympiad
2012 Paraguay Mathematical Olympiad
5
5
Part of
2012 Paraguay Mathematical Olympiad
Problems
(1)
Problem 5
Source: Paraguayan Mathematical Olympiad 2012
10/15/2012
Let
A
B
C
ABC
A
BC
be an equilateral triangle. Let
Q
Q
Q
be a random point on
B
C
BC
BC
, and let
P
P
P
be the meeting point of
A
Q
AQ
A
Q
and the circumscribed circle of
△
A
B
C
\triangle ABC
△
A
BC
. Prove that
1
P
Q
=
1
P
B
+
1
P
C
\frac{1}{PQ}=\frac{1}{PB}+\frac{1}{PC}
PQ
1
=
PB
1
+
PC
1
.
geometry
circumcircle
trigonometry
geometry proposed