A triangle ABC is inscribed in a circle If sum of the squares of sides of the triangle is equal to t...........

Quantitative Aptitude (CDS) Trignometry

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 sin² A + sin² B + sin² C is equal to

None of the above

छोटे Courses बड़े Results

Master Trignometry

Prepare through Micro-courses

Try Now

Explanation:

Remember:
If a triangle is inscribed in a circle such that the sum of the squares of sides of the triangle is equal to twice the square of diameter, then the triangle is a right-angled triangle whose hypotenuse is the same as the diameter of the circle.

In right ΔABC,
∴sin²A+sin²B+sin²C
=sin²90°+sin²B+sin²(90°−B)
=1+sin²B+cos²B
=1 +1=2 $\because$ (sin²θ+cos²θ=1)