Thursday, April 2, 2009

Problem 277: Tangent Circles, Common External Tangent

Proposed Problem

Problem 277: Tangent Circles, Common External Tangent.

See complete Problem 277 at:
gogeometry.com/problem/p277_tangent_circle_common_external_tangent.htm

Level: High School, SAT Prep, College geometry

2 comments:

  1. Join BE and draw AF perpendicular to BE meeting the latter in F. Now DE=AF and in tr. ABF: AB^2=AF^2+BF^2 or BF^2= AF^2 = BF^2 or DE^2 = AF^2 - BF^2. But AF=a+b and BF=a-b. Hence, x^2 =DF^2=(a+b)^2-(a-b)^2 or x^2 =4ab or x = 2*(ab)^(1/2)
    QED
    Ajit: ajitathle@gmail.com

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  2. (a+b)^2-(b-a)^2=x^2
    a^2+2ab+b^2-(b^2-2ab+a^2)=x^2
    4ab=x^2
    √(4ab)=x
    2√(ab)=x

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