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Contests
National and Regional Contests
Spain Contests
Spain Mathematical Olympiad
1992 Spain Mathematical Olympiad
5
5
Part of
1992 Spain Mathematical Olympiad
Problems
(1)
Brocard point in Spanish Olympiad
Source: Spanish Mathematical Olympiad 1992 P5
8/1/2018
Given a triangle
A
B
C
ABC
A
BC
, show how to construct the point
P
P
P
such that
∠
P
A
B
=
∠
P
B
C
=
∠
P
C
A
\angle PAB= \angle PBC= \angle PCA
∠
P
A
B
=
∠
PBC
=
∠
PC
A
. Express this angle in terms of
∠
A
,
∠
B
,
∠
C
\angle A,\angle B,\angle C
∠
A
,
∠
B
,
∠
C
using trigonometric functions.
geometry
Brocard
equal angles