Sunday, March 22, 2009

Problem 272. Tangent Circles, the Cube of the Common external tangent

Proposed Problem

Problem 272. Tangent Circles, the Cube of the Common external tangent.

See complete Problem 272 at:
gogeometry.com/problem/p272_tangent_circles_cube_common_external_tangent.htm

Level: High School, SAT Prep, College geometry

2 comments:

  1. In problem 271, we proved that x^3 = c*FD*GE (based upon problem 269).
    Now it's easy to see that triangles FDC & CEG are similar; hence, FD/b =a/GE or FD*GE=a*b.
    Thus, x^3 = c*a*b
    Ajit: ajitathle@gmail.com

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  2. Join FD and GE.
    Let FC + CG = c = x(a/b+b/a)
    => abc = x(a2+b2)
    => abc = x.(x2)
    Hence x3 = abc

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