If the area of an equilateral triangle inscribed in the circle x 2 + y 2 + 10 x + 12 y + c = 0 is 27 3 sq . units , then c is equal to:

Question

Aicharya · Accepted Answer

Given, area of the equilateral triangle inscribed in the circle is $27 \sqrt{3}$ , hence

$\frac{\sqrt{3}}{4} a^{2} = 27 \sqrt{3}$ $\Rightarrow a = 6 \sqrt{3} . . . (1)$

Again, $r \cos 30 ° = \frac{a}{2}$

$\Rightarrow r = 6$

Hence, the radius of a circle, $\sqrt{5^{2} + 6^{2} - c} = 6$

$\Rightarrow 25 + 36 - c = 36$

$\Rightarrow c = 25$

If the area of an equilateral triangle inscribed in the circle x 2 + y 2 + 10 x + 12 y + c = 0 is 27 3 sq .…

Solution