Points A, B, and C are on a unit circle with A and C as end points of a diameter. The midpoint of chord AB is M. If the lengths of chord AB and line segment MC are the same, what is that length?

ans: **AB=1.5118*R**

S0L:

Let AM=x and MC=2x **So** SIN(angle MCB]=.5

In triangle MCB the angle C is 30º so the angle AMC is 120º.

Applying cos law to this triangle we get:

**x²+4x²+2*x*2x*(1/2)=4R²**

7x²=4R²

........ *4/7

4x²=16*R²/7

ans**: AB=MC=2X=4*R/SQRT(7)=1.5118*R or .7559*2R**