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International Contests
IMO Longlists
1983 IMO Longlists
65
65
Part of
1983 IMO Longlists
Problems
(1)
Prove the fraction on cotangents
Source:
10/7/2010
Let
A
B
C
D
ABCD
A
BC
D
be a convex quadrilateral whose diagonals
A
C
AC
A
C
and
B
D
BD
B
D
intersect in a point
P
P
P
. Prove that
A
P
P
C
=
cot
∠
B
A
C
+
cot
∠
D
A
C
cot
∠
B
C
A
+
cot
∠
D
C
A
\frac{AP}{PC}=\frac{\cot \angle BAC + \cot \angle DAC}{\cot \angle BCA + \cot \angle DCA}
PC
A
P
=
cot
∠
BC
A
+
cot
∠
D
C
A
cot
∠
B
A
C
+
cot
∠
D
A
C
trigonometry
geometry unsolved
geometry