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12-83.

In a circle, chord has length units, while . What is the area of the circle? Draw a diagram and show all work.  

The measure of the intercepted arc is equal to the central angle.

, because both are radii, so is isosceles.

Isosceles triangles have equal base angles, so .


but ,
so

Circle, center C, with points, A, &, B, line segments from, C, to, B, from, C, to, A, from, A, to, B. Segment, A, B, labeled, 10, arc, A, B, labeled, 60 degrees.

units

Because the angles are all equal, the triangle is equilateral.

So the radius () is .