Application of maxima and minima

Question

Find the area of the smallest isosceles triangle that can be circumscribed about a circle of radius 5inches.

Answer 1

smallest isosoleez triangel=equalateral triangel (all sides the same)

Then yu wanna get the serkel INSIDE the triangel.

For equilateral triangel (oenlee equilateral) outside serkel radius=2*inside radius

outside radius=triangel side length*tan(beta)/2,

so inside radius=half this=side*tan/4

beta=30 deg for equilateral triangel, tan(30)=0.577350269

yu sae inside radius=5, so side=4*5/tan(30)

=20/0.57735

side=34.641