Saturday, July 4, 2009

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

Proposed Problem
Click the figure below to see the complete problem 314.

Problem 314.<br />Tangent circles, Common external tangent line, Geometric Mean.
See also:
Complete Problem 314
Level: High School, SAT Prep, College geometry

Posted by Antonio Gutierrez at 3:49 PM
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3 comments:

  1. VihaanJuly 18, 2009 at 1:44 AM

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

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  2. AnonymousMay 13, 2010 at 1:16 PM

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

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  3. rv.littlemanFebruary 17, 2021 at 10:14 AM

    BC^2=x^2+b^2
    From 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

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