Question

A hoop is resting vertically at staircase where AB =12 cm and BC= 8 cm .find radius of hoop?

Answer 1

If you make a center point, let's call it O, then you know that OA=OC (both radii). If you extend the line of the stair (the one parallel to the ground) out horizontally, it will eventually intersect OA. Label this point of intersection D. Now you have formed a right triangle (triangle ODC). You know that BC=AD=8. Therefore OD=OA-AD=OA-8. You also know that AB=DC=12. Using the Pythagorean theorem, you can determine the length of OC. (OA-8)^{2}+12^{2}=OC^{2}. OA^{2}-18OA+64+144 =OC^{2}. OA^{2]-18OA+208=OC^{2}. Since OC=OA (both radii), we can plug in OA for OC. OA^{2}-18OA+208=OA^{2}. Then it is merely algebra. -18OA+208=0. 18OA=208. OA=208/18. OA=104/9.