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Thread: Help with finding the radius of a circle....

  1. #1
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    Help with finding the radius of a circle....

    The problem says a chord length of 43 inches subtends a central angle of 157.8 degrees. There is a hint that says a line from the central angle is perpendicular to the chord, bisects both the angle and the chord. I have no clue how to figure this out. Thanks in advance.
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  2. #2
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    Quote Originally Posted by princesasabella View Post
    The problem says a chord length of 43 inches subtends a central angle of 157.8 degrees. There is a hint that says a line from the central angle is perpendicular to the chord, bisects both the angle and the chord. I have no clue how to figure this out. Thanks in advance.
    the chord and the two radii that intersect the chord's endpoints form a isosceles triangle with side lengths $\displaystyle r$ , $\displaystyle r$, and 43.

    law of cosines ...

    $\displaystyle 43^2 = r^2 + r^2 - 2r^2 \cos(157.8)$

    solve for $\displaystyle r$
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  3. #3
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    Hello princesasabella

    Welcome to Math Help Forum!
    Quote Originally Posted by princesasabella View Post
    The problem says a chord length of 43 inches subtends a central angle of 157.8 degrees. There is a hint that says a line from the central angle is perpendicular to the chord, bisects both the angle and the chord. I have no clue how to figure this out. Thanks in advance.
    Here's an alternative method that uses the hints you were given.

    In the attached diagram, $\displaystyle M$ bisects $\displaystyle PQ$, $\displaystyle OM$ bisects $\displaystyle \angle POQ$, and $\displaystyle OM \perp PQ$. So we have:
    $\displaystyle PM = 21.5$ in

    $\displaystyle \angle POM = 78.9^o$

    $\displaystyle \angle PMO = 90^o$
    So in $\displaystyle \triangle POM$,
    $\displaystyle \sin 78.9^o = \frac{21.5}{OP}$
    Can you solve this equation to find $\displaystyle OP$, the radius of the circle?

    Grandad
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