SOLUTION: what is the radius of a circle in which a chord 10 inches long is 1 inch from the midpoint of the arc it forms?

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Question 1156856: what is the radius of a circle in which a chord 10 inches long is 1 inch from the midpoint of the arc it forms?
Found 2 solutions by mananth, ikleyn:
Answer by mananth(16946) (Show Source):
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C is the midpoint of Arc AB.
M(arc AC) = m(arcCB)
Therefore triangle OAC congruent to triangle BOC
AC is angle bisector of therefore AC is perpendicular to AB

2r-1 = 25
2r=26
r=13

Answer by ikleyn(52925) (Show Source):
You can put this solution on YOUR website!
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Make a sketch. Find a right triangle in the sketch. Let R be the unknown radius. Then for R you have this equation (Pythagorean) R^2 = + . Simplify it r^2 = 25 + R^2 - 2R + 1 2R = 26 R = 13 inches. ANSWER

Solved.