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5
Math Prize 2023 Problem 5
Math Prize 2023 Problem 5
Source:
October 11, 2023
Problem Statement
Acute triangle
A
B
C
ABC
A
BC
has area 870. The triangle whose vertices are the feet of the altitudes of
△
A
B
C
\triangle ABC
△
A
BC
has area 48. Determine
sin
2
A
+
sin
2
B
+
sin
2
C
.
\sin^2 A + \sin^2 B + \sin^2 C .
sin
2
A
+
sin
2
B
+
sin
2
C
.
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