Proposed Problem

See complete Problem 272 at:

gogeometry.com/problem/p272_tangent_circles_cube_common_external_tangent.htm

Level: High School, SAT Prep, College geometry

## Sunday, March 22, 2009

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

Labels:
circle,
common tangent,
cube,
diameter,
tangency point,
tangent

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In problem 271, we proved that x^3 = c*FD*GE (based upon problem 269).

ReplyDeleteNow 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

Join FD and GE.

ReplyDeleteLet FC + CG = c = x(a/b+b/a)

=> abc = x(a2+b2)

=> abc = x.(x2)

Hence x3 = abc