Let `C`,`C_1`,`C_2` be circles of radii 5,3,2 respectively. `C_1` and `C_2`, touch each other externally and C internally. A circle `C_3` touches `C_1` and `C_2` externally and C internally. If its radius is `m/n` where m and n are relatively prime positive integers, then 2n-m is:

3 circles of radii a, b, c (a lt b lt c) touch each other externally and have x-axis as a common tangent then

C_1 and C_2 are fixed circles of radii r_1 and r_2 touches each other externally. Circle 'C' touches both Circles C_1 and C_2 extemelly. If r_1/r_2=3/2 then the eccentricity of the locus of centre of circles C is

Let C_1 and C_2 be two circles with C_2 lying inside C_1 A circle C lying inside C_1 touches C_1 internally and C_2 externally. Identify the locus of the centre of C

There are two circles C_(1) and C_(2) touching each other and the coordinate axes, if C_(1) is smaller than C_(2) and its radius is 2 units, then radius of C_(2) , is

Let A B C be a triangle right-angled at Aa n dS be its circumcircle. Let S_1 be the circle touching the lines A B and A C and the circle S internally. Further, let S_2 be the circle touching the lines A B and A C produced and the circle S externally. If r_1 and r_2 are the radii of the circles S_1 and S_2 , respectively, show that r_1r_2=4 area ( A B C)dot

A circle C_1 of radius b touches the circle x^2 + y^2 =a^2 externally and has its centre on the positiveX-axis; another circle C_2 of radius c touches the circle C_1 , externally and has its centre on the positive x-axis. Given a lt b lt c then three circles have a common tangent if a,b,c are in

A relation R is defined on the set of circles such that " C_(1)RC_(2)implies circle C_(1) and circle C_(2) touch each other externally", then relation R is

Let C_1 and C_2 be two circles with C_2 lying inside C_1 . A circle C lying inside C_1 touches C_1 internally and C_2 externally. Statement : 1 Locus of centre of C is an ellipse. Statement (2) The locus of the point which moves such that the sum of its distances from two fixed points is a constant greater than the distance between the two fixed points is an ellipse. (A) Both 1 and 2 are true and 2 is the correct explanation of 1 (B) Both 1 and 2 are true and 2 is not a correct explanation of 1 (C) 1 is true but 2 is false (D) 1 is false but 2 is true

Three circles C_(1),C_(2),C_(3) with radii r_(1),r_(2),r_(3)(r_(1)ltr_(2)ltr_(3)) respectively are given as r_(1)=2 , and r_(3)=8 they are placed such that C_(2) lines to the right of C_(1) and touches it externally C_(3) lies ot the right of C_(2) and touches it externally. There exist two stratight lines each of whic is a direct common tangent simultaneously to all the three circles then r_(2) is equal to

The centres of two circles C_(1) and C_(2) each of unit radius are at a distance of 6 unit from each other. Let P be the mid-point of the line segment joining the centres of C_(1) and C_(2) and C be a circle touching circles C_(1) and C_(2) externally. If a common tangent to C_(1) and C passing through P is also a common tangent to C_(2) and C, then the radius of the circle C, is