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From: "kamuran turksoy" <kamuranturksoy@gmail.com>
Newsgroups: comp.soft-sys.matlab
Subject: Intersection of two Disks
Date: Fri, 5 Oct 2012 20:33:08 +0000 (UTC)
Organization: illinois Institute of technology
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I have two disks:
C1: (x-a1)^2+(y-b1)^2<=r1^2
C2: (x-a2)^2+(y-b2)^2<=r2^2

These disks have non-empty intersection.

I define the third circle as:
C3: (x-a3)^2+(y-b3)^2<=r3^2    where

a3=a1*(1-t)+a2*t
b3=b1*(1-t)+b2*t
r3=sqrt(a3^2+b3^2-(a1^2+b1^2-r1^2)*(1-t)-(a2^2+b2^2-r2^2)*t)
where 0<=t<=1.

Claim: C3 contains the intersection of C1 and C3 for all values of t such that 0<=t<=1

Numerically when i substitute t values and check it the claim works. However i could not prove it. Any suggestions?

Regards