Thursday, March 19, 2009

Problem 271. Tangent Circles, the Cube of the Common external tangent

Proposed Problem

Problem 271. Tangent Circles, the Cube of the Common external tangent.

See complete Problem 271 at:
gogeometry.com/problem/p271_tangent_circles_cube_common_external_tangent.htm

Level: High School, SAT Prep, College geometry

2 comments:

  1. Extend FD & GE to meet in H. HFG is a rt. angled triangle where HC is perpendicular to FG. Also CH = DE = h both being diagonals of the rectangle CEHD. Now we've proven in Problem 269 that x^3 = CH^3 = h^3 = c*FD*GE.
    Hence, x^3 = c*a*b
    Ajit: ajitathle@gmail.com

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  2. If you do not wish to refer to any earlier problem then with the construction as b4, a*FH=FC^2 & b*GH=CG^2 from where a*b=(FC*CG)^2/(FH*GH). But from Tr.FHG, FH*GH=HC*FG=x*c and FC*CG=x^2. Hence, a*b=(x^4)/(x*c) or x^3 =abc
    Ajit

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