The circumference of a circle is 36 pi inches. What is the length of the radius of this circle?

Radius 18in

Step-by-step explanation:

Perimeter of circle =2×pi×r, where r is the radius.

36×pi=2×pi×r

r=36/2=18in

9 x 8 divided by (5-3)=36

we have three similar triangles, because each has a right angle and shares an angle.   let's write the angles in order: opposite to short leg, long leg, hypotenuse.

cab similar to bad similar to cbd

or as ratios,

ca: ab: cb = ba: ad: bd = cb: bd: cd

we also know

ac = ad + cd

(ad+cd): ab: cb = ba: ad: bd = cb: bd: cd

(ad+cd)/cb=cb/cd

we have cb=6, ad=5 and seek x=cd.

we reject the negative root and conclude x=4

answer: 4