Tuesday, March 17, 2009

Problem 270. Tangent Circles, Common external tangent, Fractional exponents

Proposed Problem

Problem 270. Tangent Circles, Common external tangent, Fractional exponents

See complete Problem 270 at:
gogeometry.com/problem/p270_tangent_circles_fractional_exponent.htm

Level: High School, SAT Prep, College geometry

1 comment:

  1. Extend FD & GE to meet in H. HFG is a rt. angled triangle where HC is perpendicular to FG. Now by the previous problem (no. 269) we've:
    a = FH^3/x^2 & b = GH^3/x^2.
    Thus, a^(2/3)+ b^(2/3)=(FH^3/x^2)^(2/3)+ (GH^3/x^2)^(2/3)=(FH^2+GH^2)/x^(4/3)
    = x^2/x^(4/3) = x^(2/3)
    or a^(2/3) + b^(2/3)= x^(2/3)
    Ajit: ajitathle@gmail.com

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