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

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

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?

Two circles C_1 and C_2 intersect at two distinct points P and Q in a line passing through P meets circles C_1 and C_2 at A and B , respectively. Let Y be the midpoint of A B and Q Y meets circles C_1 and C_2 at X a n d Z respectively. Then prove that Y is the midpoint of X Z

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 (a) 2sqrt(3)-3 (b) 2sqrt(2)-1 (c) 2sqrt(2)-1 (d) 1

Let C_(1) and C_(2) denote the centres of the circles x^(2) +y^(2) = 4 and (x -2)^(2) + y^(2) = 1 respectively and let P and Q be their points of intersection. Then the areas of triangles C_(1) PQ and C_(2) PQ are in the ratio _

Let be the circle with centre at (1 , 1) and radius is 1 unit . It T is the circle centred at (0 , y) , passing through origin and touching the circle c externally , then the radius of T is equal to _

Suppose that two circles C_(1) and C_(2) in a plane have no points in common. Then

Let C_1 and C_2 be two circles whose equations are x^2+y^2-2x=0 and x^2+y^2+2x=0 and P(lambda, lambda) is a variable point . List 1 a) P lies inside C_1 ​ but outside C_2 ​ b)P lies inside C_2 ​ but outside C_1 ​ c)P lies outside C_1 ​ but outside C_2 ​ d)P does not lie inside C_2 ​ List 2 p)λ ϵ (−∞,−1)∪(0,∞) q)λ ϵ (−∞,−1)∪(1,∞) r)λ ϵ (−1,0) s)λ ϵ (0,1)