I've got a section of a circle; kind of a slice off the edge. It's 84" wide and comes out 10" in the center.

Question

How can I calculate the radius?

Answer 1

if i am understanding the shape of the slice i calculate the radius of the circle to be 93.2" I used the pathegorean theorem for right triangles but it is hard to illustrate without a drawing

***UPDATE****
chavo has the right idea but he used the wrong triangle...how could you have the chord of a circle be 84" when his diameter is 86.4" and only have a slice?

***UPDATE #2****
ok this is how i solved it without using rules of chords.
Call the midpoint of the chord pt A and the end of the chord pt B and the center of the circle pt C.
From pt A to pt B is 42"
From pt B to pt C is the radius of the circle (r)
From pt A to pt C is r-10 (since it is 10" from A to the edge of the circle)
The angle at pt A is a right angle so we can use the pathegorean theorem where r is the hypotenuse.
so:
(r-10)^2 + 42^2=r^2
r^2 -20r+100 +1764=r^2
simplifies to: -20r + 1864=0
r=93.2

Answer 2

Draw the circle and the chord that slices off the arc. Draw radii from each end of the arc and from the center of the arc. Let the center of the circle be O, left end of the arc (and chord) A, right end B, center point of the arc C, and name intersection of chord AB and radius CO D. And on the other side of the circle, radius CO intersects the circle at E.

AB and CE are intersecting chords, so AD•DB = CD•DE. AD = DB = 42. Since OE is a radius, let OE = r. Then CD = 10 and DE = r + r - 10 = 2r - 10. So we have

42•42 = 10(2r - 10)
1764 = 20r - 100
1864 = 20r
r = 93.2 inches.

Answer 3

If I am interpreting the problem correctly, you have a circle, with a chord of length 84. The distance from the center to the midpoint of the chord is 10. The line of length 10 forms a right angle with the chord. Draw a right triangle and use the Pythagorean Theorem. One leg of the triangle will be 42'' in length because the chord is split in half by the line of length 10.
r^2 = 10^2 + 42^2
r = sqrt (100 + 1764)
r = sqrt (1864)
Answer: r = 43.2 inches

Answer 4

Can't understand your question, can you please state it as it is written?