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
SPOILER
