2015 · Q75
A triangle ABC is inscribed in a circle. If sum of the squares of sides of the triangle is equal to twice the square of the diameter, then ²A+²B+²C is equal to
Elementary MathematicsGeometry: Lines, Angles and Triangles
- A2
- B3
- C4
- DNone of the above
Explanation
This combines the sine rule with the given condition. With circumradius R, the sides are a = 2R sin A, etc., so sin²A + sin²B + sin²C = (a² + b² + c²)/4R². The condition says a² + b² + c² = 2(2R)² = 8R², so the sum is 8R²/4R² = 2. Option (b) 3 is the trap from confusing this with a cosine-squared identity. Hence option (a).