The length of an arc - Math Central

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Question from Chris:

trying to find the length of an arc or segment of a circle when the radius or circumference is unknown
take a circle, put a line across the circle label it A /B /C
A and C are the end points, B is the middle
line length is 86. From B to the side of circle is 16. Label that point D
need to find the length of A D C

Hi Chris,

circle

P is the centre of the circle. Let r be the radius of the circle then in the diagram |PB| = r - 16. Triangle CBP is a right triangle so by Pythagoras theorem

43² + (r - 16)² = r²

Solve for r.

If you have r can you find the length of the arc ADC?

Penny

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