Let `C_(1)andC_(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. Idenitfy the locus of the center 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

t_(1),t_(2),t_(3) are lengths of tangents drawn from a point (h,k) to the circles x^(2)+y^(2)=4,x^(2)+y^(2)-4x=0andx^(2)+y^(2)-4y=0 respectively further, t_(1)^(4)=t_(2)^(2)" "t_(3)^(2)+16 . Locus of the point (h,k) consist of a straight line L_(1) and a circle C_(1) passing through origin. A circle C_(2) , which is equal to circle C_(1) is drawn touching the line L_(1) and the circle C_(1) externally. The distance between the centres of C_(1)andC_(2) is

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 its centre is :

t_(1),t_(2),t_(3) are lengths of tangents drawn from a point (h,k) to the circles x^(2)+y^(2)=4,x^(2)+y^(2)-4x=0andx^(2)+y^(2)-4y=0 respectively further, t_(1)^(4)=t_(2)^(2)" "t_(3)^(2)+16 . Locus of the point (h,k) consist of a straight line L_(1) and a circle C_(1) passing through origin. A circle C_(2) , which is equal to circle C_(1) is drawn touching the line L_(1) and the circle C_(1) externally. Equation of C_(1) is

t_(1),t_(2),t_(3) are lengths of tangents drawn from a point (h,k) to the circles x^(2)+y^(2)=4,x^(2)+y^(2)-4=0andx^(2)+y^(2)-4y=0 respectively further, t_(1)^(4)=t_(2)^(2)" "t_(3)^(2)+16 . Locus of the point (h,k) consist of a straight line L_(1) and a circle C_(1) passing through origin. A circle C_(2) , which is equal to circle C_(1) is drawn touching the line L_(1) and the circle C_(1) externally. Equation of L_(1) is

Let C be the circle with centre at (1, 1) and radius = 1. If 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

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

Consider the two circles C_(1):x^(2)+y^(2)=a^(2)andC_(2):x^(2)+y^(2)=b^(2)(agtb) Let A be a fixed point on the circle C_(1) , say A(a,0) and B be a variable point on the circle C_(2) . The line BA meets the circle C_(2) again at C. 'O' being the origin. If (BC)^(2) is maximum, then the locus of the mid-piont of AB is

C_1 and C_2 are two concentric circles, the radius of C_2 being twice that of C_1 . From a point P on C_2 , tangents PA and PB are drawn to C_1 . Prove that the centroid of the triangle PAB lies on C_1 .

If C_(1): x^(2)+y^(2) =(3+2sqrt(2))^(2) be a circle. PA and PB are 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 PA and PB is