From any point on one given circle tangents are drawn to another given circle, prove that the locus of the middle point of the chord of contact is a third circle

The locus of the mid points of all equal chords in a circle is :

From points on the circle x^2+y^2=a^2 tangents are drawn to the hyperbola x^2-y^2=a^2 . Then, the locus of mid-points of the chord of contact of tangents is:

Tangents are drawn to a unit circle with centre at the origin from each point on the line 2x+y=4. Then the equation to the locus of the middle point of the chord of contact is

If from any point on the common chord of two intersecting circles,tangents be drawn to the circles,prove that they are equal.

Director circle || Equation OF chord with a givin middle point ,chord OF contact

From the origin,chords are drawn to the circle (x-1)^(2)+y^(2)=1. The equation of the locus of the mid-points of these chords is circle with radius

Through a fixed point (h, k) secants are drawn to the circle x^(2) + y^(2) =a^(2) . The locus of the mid points of the secants intercepted by the given circle is