In the figure, L is the centre of the circle, and ML is the perpendicular to LN. If the area of the triangle MLN is 36, then the area of the circle is:

72π

We know that,

Area of the circle = πr²

Area of the right-angled triangle = (1/2) × Base × Height

In ΔLMN

LM = LN = radius

Area of right-angled ΔLMN = \(\frac{1}{2}\)  × r × r

= 36 = \(\frac{r^2}{2}\) 

= r² = 72

Area of the circle = πr² = 72π