If lx + my = 1 touches the circle `x^2 + y^2 = a^2`, prove that the point (l, m) lies on the circle `x^2 + y^2 = a^(-2)`

If the chord of contact of tangents from a point on the circle x^(2) + y^(2) = a^(2) to the circle x^(2)+ y^(2)= b^(2) touches the circle x^(2) + y^(2) = c^(2) , then a, b, c are in-

If the line hx+ky=1 touches x^2+y^2=a^2 , then the locus of the point (h,k) is a circle of radius

The circle x^2 + y^2 - 8x + 4y +4 = 0 touches

The centre of a circle passing through the points (0,0),(1,0)and touching the circle x^2+y^2=9 is

The circle (x+2)^(2) + (y-3)^(2) = 4 touches -

The chord of contact of tangents drawn from a point on the circle x^2 + y^2 = a^2 to the circle x^2 + y^2 = b^2 touches the circle x^2 + y^2=c^2 Show that a, b, c are in G.P.

Equation of a circle with centre (4, 3) touching the circle x^2+y^2=1 is

The pole of a straight line with respect to the circle x^2+y^2=a^2 lies on the circle x^2+y^2=9a^2 . If the straight line touches the circle x^2+y^2=r^2 , then :

If y = mx is the equation of a chord of the circle x^2+y^2-2ax=0 with radius a, prove that the equation of the circle on this chord as a diameter is (1+m^2)(x^2+y^2)-2a(x + my)=0 .

A tangent at a point on the circle x^2+y^2=a^2 intersects a concentric circle C at two points Pa n dQ . The tangents to the circle X at Pa n dQ meet at a point on the circle x^2+y^2=b^2dot Then the equation of the circle is (a) x^2+y^2=a b (b) x^2+y^2=(a-b)^2 (c) x^2+y^2=(a+b)^2 (d) x^2+y^2=a^2+b^2