Two parallel tangents to a given circle are cut by a third tangent at the point `Ra n dQ` . Show that the lines from `Ra n dQ` to the center of the circle are mutually perpendicular.

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

A Tangent to a circle is a line which touches the circle at only one point.

The lengths of the two tangents from an external point to a circle are equal.

The tangent at any point of a circle is perpendicular to the radius through the point of contact.

The tangent at any point on the curve x=acos^3theta,y=asin^3theta meets the axes in Pa n dQ . Prove that the locus of the midpoint of P Q is a circle.

Fill in the blanks Prove that the tangents to a circle at the end points of a diameter are parallel.

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

The chord of contact of tangents from a point P to a circle passes through Qdot If l_1a n dl_2 are the length of the tangents from Pa n dQ to the circle, then P Q is equal to

Perpendiculars are drawn, respectively, from the points Pa n dQ to the chords of contact of the points Qa n dP with respect to a circle. Prove that the ratio of the lengths of perpendiculars is equal to the ratio of the distances of the points Pa n dQ from the center of the circles.