NDA2017MathematicsApplication of DerivativesActual
What is the maximum area of a triangle that can be inscribed in a circle of radius a?
Options
- A3 a ^2 4
- Ba ^2 2
- C3 3 a ^2 4
- D3 a^2 4
Correct answer
C. 3 3 a ^2 4
Step-by-step solution
For area of triangle to be maximum, it should be equilateral triangle. Area of OAB = 1 2 ab = 1 2 a a = 1 2 a ^2 120^ = 3 4 a ^2 Area of triangle OAB , OBC , OAC = Area of triangle ABC aligned & =3 3 4 a^2 & = 3 3 4 a^2 aligned