(iii)If two circles cut a third circle orthogonally; then the radical axis of two circle will pass through the center of the third circle .

The radical axis of two circles S=0, S'=0 does not exist if

If z!=1 and (z^2)/(z-1) is real, then the point represented by the complex number z lies (1) either on the real axis or on a circle passing through the origin (2) on a circle with centre at the origin (3) either on the real axis or on a circle not passing through the origin (4) on the imaginary axis

If z!=1 and (z^2)/(z-1) is real, then the point represented by the complex number z lies (1) either on the real axis or on a circle passing through the origin (2) on a circle with centre at the origin (3) either on the real axis or on a circle not passing through the origin (4) on the imaginary axis

Two parallel tangents to a given circle are cut by a third tangent at the points Aa n dBdot If C is the center of the given circle, then /_A C B (a)depends on the radius of the circle. (b)depends on the center of the circle. (c)depends on the slopes of three tangents. (d)is always constant

Two circles with equal radii are intersecting at the points (0, 1) and (0,-1). The tangent at the point (0,1) to one of the circles passes through the centre of the other circle. Then the distance between the centres of these circles is.

Three circles with radii 1,2 and 3 inches are externally tangent to one another , as shown in the figure above . The area , in square inches , of the sector of the circle of radius 1 that is cut off by the line segments joining the center of that circle to the centers of the other two circles (the shaded area ) is

If the chord of contact of tangents from a point P to a given circle passes through Q , then the circle on P Q as diameter. cuts the given circle orthogonally touches the given circle externally touches the given circle internally none of these

The centres of the circles are (a, c) and (b, c) and their radical axis is y-axis. The radius of one of the circles is r. The radius of the other circle is

(a,0) and (b, 0) are centres of two circles belonging to a co-axial system of which y-axis is the radical axis. If radius of one of the circles 'r', then the radius of the other circle is