Proposed Problem

See complete Problem 279 at:

gogeometry.com/problem/p279_tangent_circle_common_external_tangent_chord_inradius.htm

Level: High School, SAT Prep, College geometry

## Thursday, April 2, 2009

### Problem 279: Tangent Circles, Common External Tangent, Chords, Inradius

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Using results from earlier problems, we know that: CD^2 = 4ba^2/(a+b), CE^2=4ab^2/(a+b) and DE^2=4ab. Further, r=CD*CE/(CD+CE+DE)

ReplyDeleteThus,r=(2aVb*2bVa)/(2aV(b/(a+b))+2aV(a/(a+b))+2V(ab)) where V = square root

Thus, r = [4abV(ab/(a+b))]/2aVb+2bVa+2V(ab(a+b)

Upon rationalization & simplification it can easily be show that:

r=Vab[Va+Vb-V(a+b)]/V(a+b) or

r=V(ab)[(Va+Vb)V(a+b) -1]

QED

Ajit: ajitathatle