Question bank/JEE Main/Mathematics

The centers of two circles C_1and C_2 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 centers of C_1and C_2 be a circle touching
circles C_1and C_2 externally. If a common tangent to C_1and C
passing through P is also a common tangent to C_2 and C, then the
radius of the circle C is
bdkbZ f=T;k okys nks o`Ùkksa C_1 rFkk C_2 Uæ,d nwljs ls 6 bdkbZ
nwjh ij gSaA ekuk fd C_1 rFkk C_2 Uæksa okys
fcUnq P

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[IMAGE] $$r^{2} + 8 = + 2r + 1 = + 8 + 92r = 16\ \ \ \ \Rightarrow \ \ \ \ r = 8$$

Source: Grass-G / M-26 Mathematics Paper 1 15 Jan.docx