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): You can put this solution on YOUR website!
.

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(52932)   (Show Source): You can put this solution on YOUR website!
.

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.



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