If the arc length and chord length between two points

nrgiizr0ib6

nrgiizr0ib6

Answered question

2022-04-30

If the arc length and chord length between two points (two points on a circle that constitute a minor arc ) in a circle are known , find radius of the circle?

Answer & Explanation

Dexter Conner

Dexter Conner

Beginner2022-05-01Added 15 answers

If the O is the center of the circle, A and B are the end points of the chord and arc, then et α be an angle A O B.

Let also c - the length of the arc and b - the length of A B, d - diameter. Then we know that
α d / 2 = c ,
d sin ( α / 2 ) = b ,
or
sin ( c d ) = b d .
If x = c d , then you are to solve an equation
sin x = b c x .

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