Consider a circle with radius 1 and center $O$. Points $A, B $ are on the circumference such that $ \angle AOB = \frac{ \pi}{3} $.

What is the radius of the largest circle that can be inscribed in sector $AOB $?

Guest Oct 26, 2019

#1**+1 **

A circle has 2 radians

Since AOB is \(\frac{\pi}{3}\)

AOB is 60 degrees.

AOB forms an equilateral triangle.

Find the largest circle that fits in a equilateral triangle with sides of 1.

The formula -> \(A=rs\)

S is semi pereimeter while the R means radius.

So we solve for R. \(r=\frac{A}{s}\)

Semi perimeter is 1 + 1 + 1 = 3

3/2 = 1.5

The area of an equilateral triangle is \(\frac{\sqrt{3}}{4}a^2\), where a is the length of one side.

So the area is \(\frac{\sqrt{3}}{4}\).

Ok now we evaluate. \(\frac{\frac{\sqrt{3}}{4}}{1.5}\).

\(\frac{\sqrt{3}}{6}\) that is the answer I think

CalculatorUser Oct 26, 2019