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# helpp

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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 $AOB$?

Oct 26, 2019

#1
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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

Oct 26, 2019