Let `C_1 and C_2` be externally tangent circles with radius 2 and 3 respectively. Let `C_1 and C_2` both touch circle `C_3` internally at point A and B respectively. The tangents to `C_3` at A and B meet at T and TA = 4, then radius of circle `C_3` is :

If tangent at (1,2) to the circle x^(2)+y^(2)=5 intersect the circle x^(2)+y^(2)=9 at A and B and tangents at A and B meets at C. Find the coordinate of C

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.

C_(1) and C_(2) are two concentric circles with centres at O. Their radii are 12 cm and 3 cm respectively. B and C are the points of contact of two tangents draw to C_(2) from a point A lying on the circle C_(1) . Then the area of the quadrilateral ABOC is-

The centres of two circles C_1 and 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 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.

C_(1) and C_(2) are two concentric circles with centres at O. Their radii are 12 cm and 3 cm respectively. B is the point of contact of tangents drawn to C_(2) from a point A lying on the circle C_(1) . Then the area of the triangle OAB is :

Let nge3 and let C_1, C_2, ...., C_n, be circles with radii r_1, r_2,... r_n, respectively. Assume that C_i and C_(i+1) touch externally for 1leilen-1. It is also given that the x-axis and the line y = 2sqrt(2)x+10 are tangential to each of the circle . Then r_1,r_2.r_n are in (A) an arithmetic progression with common difference 3+sqrt(2) (B) a geometric progression with common ratio 3+sqrt(2) (C) an arithmetic progression with common difference 2+sqrt(3) (D) a geometric progression with common ratio 2+sqrt(3)

Two circles with radii a and b respectively touch each other externally . Let c be the radius of a circle that touches these two circles as well as a common tangent to the circles. Then

Let C_(1), C_(2) be two circles touching each other externally at the point A and let AB be the diameter of circle C_(1) . Draw a secant BA_(3) to circle C_(2) , intersecting circle C_(1) at a point A_(1)(neA), and circle C_(2) at points A_(2) and A_(3) . If BA_(1) = 2 , BA_(2) = 3 and BA_(3) = 4 , then the radii of circles C_(1) and C_(2) are respectively