Conic Sections : Challenge #2

Geometry Level 2

Sub-unit: Circles

The centre of two circles C1 and C2 each of unit radius are at a distance of 6 units from each other. Let P be the mid point of the line segment joining the centres of C1 and C2 and C be a circle touching circles C1 and C2 externally. If a common tangent to C1 and C passing through P is also a common tangent to C2 and C , then the radius of the circle C is :


The answer is 8.

Ninad Akolekar by Ninad Akolekar , 23, India

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1 solution

Deepanshu Gupta
Jan 27, 2015

Let C 1 ( 3 , 0 ) & C 2 ( − 3 , 0 ) & C ( 0 , α ) \displaystyle{{ C }_{ 1 }(3,0)\quad \& \quad { C }_{ 2 }(-3,0)\quad \& \quad C(0,\alpha )}
and use Pythagoras and see The MAGIC ! ⌣ ¨ \ddot\smile

5 Helpful 0 Interesting 0 Brilliant 0 Confused

Thanks Deepanshu, for such a nice solution.

That's JEE approach, as my teacher would say to me.

And I like such methods. You cannot always rely upon the theoretical and bookish solutions of such problems, although this doesn't mean that the generalized method isn't important.

By adopting such methods not only you reach to correct answer quickly, but also you get an idea about the actual proof/solution of the result/problem.

Also post solutions to my other challenges, if you have solved those with such methods, especially.

Ninad Akolekar - 6 years, 4 months ago

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