Find the smallest possible area of an isosceles triangle that is circumscribed about a circle of radius $r=4$ .
A) $4 \pi \sqrt{3}$
B) $4 \sqrt{3}$
C) $48 \sqrt{3}$
D) $\sqrt{3}$
E) $\sqrt{48} r^{2}$

Question

Quizplus · Accepted Answer

The smallest area of an isosceles triangle circumscribed about a circle is achieved when the triangle is equilateral. For an equilateral triangle with a circle of radius $ r $ inscribed, the side length $ s $ is $ 2r\sqrt{3} $. The area $ A $ of the triangle is $ \frac{\sqrt{3}}{4} s^2 = \frac{\sqrt{3}}{4} (2r\sqrt{3})^2 = 48\sqrt{3} $.

Find the Smallest Possible Area of an Isosceles Triangle That r=4r=4r=4

Find the Smallest Possible Area of an Isosceles Triangle That $r=4$