MathDB
Problems
Contests
National and Regional Contests
Poland Contests
Polish MO Finals
1950 Polish MO Finals
5
5
Part of
1950 Polish MO Finals
Problems
(1)
sin^2 A+sin^2 B +sin^2 c=2 iff ABC is right triangle
Source: Polish MO Finals 1950 p5
9/1/2024
Prove that if for angles
A
,
B
,
C
A,B,C
A
,
B
,
C
of a triangle holds
sin
2
A
+
sin
2
B
+
sin
2
C
=
2
\sin^2 A+\sin^2 B +\sin^2 C=2
sin
2
A
+
sin
2
B
+
sin
2
C
=
2
iff the triangle
A
B
C
ABC
A
BC
is right.
trigonometry
geometry
right triangle
right angle