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 June 22nd, 2012, 09:43 AM #1 Member   Joined: Oct 2011 Posts: 81 Thanks: 0 distinct points on a circle Ques 1- If $(m_i,1/m_i), m_i>0,$i=1,2,3,4 are four distinct points on a circle, then show that m1*m2*m3*m4=1. Ques 2- Three circles touch each other externally. The tangents at their points of contact meet at a point whose distance from any point of contact is 4. Find the ratio of product of radii to the sum of radii of the circles. Pls help in answering these questions. Thanks!
 June 22nd, 2012, 11:07 AM #2 Member   Joined: Jun 2012 From: UK Posts: 39 Thanks: 0 Re: distinct points on a circle
 June 24th, 2012, 04:59 AM #3 Global Moderator   Joined: Dec 2006 Posts: 20,835 Thanks: 2162 Q2.  The distance 4 is the inradius of the triangle whose vertices are the centres of the three circles. Choose variables for the radii of the circles, then equate the area of that triangle as given by Heron's formula and this formula. The required ratio is then easily obtained.

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