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June 22nd, 2012, 09:43 AM   #1
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distinct points on a circle

Ques 1- If 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.
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June 22nd, 2012, 11:07 AM   #2
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Re: distinct points on a circle

Q1

See First page of Googling
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June 24th, 2012, 04:59 AM   #3
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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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