Proposed Problem

Click the figure below to see the complete problem 314.

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Complete Problem 314

Level: High School, SAT Prep, College geometry

## Saturday, July 4, 2009

### Problem 314. Tangent circles, Common external tangent line, Geometric Mean.

Labels:
circle,
common tangent,
geometric mean

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Draw a line BE parallel to DC meeting AC in E. Thus, AE = a - b and AB = a + b

ReplyDeleteFrom rt. angled tr. AEB CD^2 = x^2 = AB^2 – AE^2 = (a+b)^2 –(a-b)^2 = 4ab Or x = 2V(ab) QED

Vihaan: vihaanup@gmail.com

Could you find the length of a if you knew the length of x and b?

ReplyDeleteBC^2=x^2+b^2

ReplyDeleteFrom law of cosines :

BC^2=a^2+(a+b)^2-2a(a-b)

x^2+b^2=2a^2+2ab+b^2-2a^2+2ab

Therfore

x^2=4ab