Question

The area of an equilateral triangle inscribed in the circle x^2+y^2=a2

Answer 1

Answer:x2 + y2 - 6x + 2y - 15 = 0

Centre O = (3, -1)

radius r = √{32 + (-1)2 -(-15)} = √{9 + 1 + 15 } = √25 = 5

Also ∠OBD = 60

From right angle triangle OBD,

     sin 60 = BD/OB

=> √3/2 = BD/r

=> BD = r*√3/2

Also, BC = 2*BD = 2*r*√3/2 = √3r

Now, area of the triangle ABC = √3/4 * a2    {a is the side of the triangle ABC}

Step-by-step explanation: