3 tangent circles

JEE Advanced 2015 Answers › Co-ordinate Geometry questions › 3 tangent circles

C₁,C₂ and C₃ are 3 tangent circles, these circle tangent to a line too. If the radius of C₁ is 9 and radius of C₂ is 4. Find the raduis of c₃.

#Mathematics #Co-ordinate Geometry

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6 Answers

262

Aditya Bhutra ·2011-12-23 07:41:26

what are tangent circles?

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fahadnasir nasir ·2011-12-23 08:08:43

Tangent circles may be tangent either internally or externally. Tangent circles are tangent internally if one lies in the interior of the other (except for the point of tangency). Tangent circles are tangent externally if each lies in the exterior of the other (except for the point of tangency). The figure below shows tangent circles with external and internal tangents

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Vivek @ Born this Way ·2011-12-24 01:06:25

If these are tangent cirlces, then anything is possible for third circle? isn't it?

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fahadnasir nasir ·2011-12-24 02:05:39

Viv. the question is that all circles are in external tangency.

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Vivek @ Born this Way ·2011-12-24 06:52:28

In that case, the line could be tangent only to two circles . Is it?

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fahadnasir nasir ·2011-12-24 09:28:28

No. The 3 circles are tangent. but they don't have the same tangent point.

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