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

A circle is given by x^2 + (y-1) ^2 = 1 , another circle C touches it externally and also the x-axis, then the locus of center 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

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

C1 and C2 are two concentric circles, the radius of C2 being twice that of C1. From a point P on C2, tangents PA and PB are drawn to C1. Then the centroid of the triangle PAB (a) lies on C1 (b) lies outside C1 (c) lies inside C1 (d) may lie inside or outside C1 but never on C1

Consider three circles C_1, C_2 and C_3 such that C_2 is the director circle of C_1, and C_3 is the director circlé of C_2 . Tangents to C_1 , from any point on C_3 intersect C_2 , at P^2 and Q . Find the angle between the tangents to C_2^2 at P and Q. Also identify the locus of the point of intersec- tion of tangents at P and Q .

If C_1: x^2+y^2=(3+2sqrt(2))^2 is a circle and P A and P B are a pair of tangents on C_1, where P is any point on the director circle of C_1, then the radius of the smallest circle which touches c_1 externally and also the two tangents P A and P B is 2sqrt(3)-3 (b) 2sqrt(2)-1 2sqrt(2)-1 (d) 1

In the figure given, two circles with centres C_t and C_2 are 35 units apart, i.e. C_1 C_2=35 . The radii of the circles with centres C_1 and C_2 are 12 and 9 respectively. If P is the intersection of C_1 C_2 and a common internal tangent to the circles, then l(C_1 P) equals

A circle C_1 , of radius 2 touches both x -axis and y - axis. Another circle C_2 whose radius is greater than 2 touches circle and both the axes. Then the radius of circle is

Let C be the circle with centre at (1,1) and radius =1 . If T is the circle centered at (0,y) passing through the origin and touching the circle C externally. Then the radius of T is equal to