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The radius of a circle with 12 = cords of 3.75"

I am calculating a circluar bolt patern and need the radius on the circle with 12 bolts spaced 3.75"  (cord) apart

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2 Answers

You can also use law of sines to get R.

R/sin75 = 3.75/sin30

R = sin75(3.75/sin30) = 7.244 inches

The chord is the base of an isosceles triangle, the equal sides of which are radii. The central angle of the triangle is 30 degrees because there are 12 equal arcs. A perpendicular from the apex to the base yields a right triangle, with angles of 15 degrees and 75 degrees. The length of a side is a radius. It can be calculated by using the formula R = 1.875/sin 15 degrees. 

The answer is 7.24 inches.

Comments

Revision to above answer: I didn't see that the Chord length was 3.75, not the arc length. The correct answer for the radius is 7.24 inches, calculated by usiing sin (15 degrees) = 1.875/radius. Thus radius = 1.875/.2588 = 7.24.