Geometry Problem. Post your solution in the comments box below.

Level: Mathematics Education, High School, Honors Geometry, College.

Click the figure below to see the complete problem 985.

## Monday, February 17, 2014

### Geometry Problem 985: Circle, Radius, Perpendicular, Concentric Circles, Congruence, Triangle

Labels:
circle,
concentric circles,
congruence,
perpendicular,
radius,
triangle

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1. CD/OA = EG/OF

ReplyDelete2. CD/OA = CD/OB = CE/OE = AF/OF

Thus, AF=EG.

Let R, r denote the radii of the outer and inner concentric circles.

ReplyDeleteNow EG / r = EG / OB = DG / OD = EG / OB = CE / OC = AF / r

since AF = OF - OA = R - r = OE - OC = CE.

Hence EG = AF

If R and r are the radii of the larger and smaller circles respectively, then from similar triangles,

ReplyDeleteR/OG = r/OD = EG/DG

Hence EG = r.(DG/OD) = r. (OG-OD)/OD = r.(OG/OD - 1) = r.(R/r - 1) = R-r = AF

Sumith Peiris

Moratuwa

Sri Lanka