P and P' are corresponding points on an ellipse and its auxilliary circle. Prove that the tangents at P and P' intersect on the major axis.

A tangent at a point on the circle x^(2)+y^(2)=a^(2) intersects a concentrie circle S at P and Q. The tangents to S at P and Q meet on the circle x^(2)+y^(2)=b^(2) . The equation to the circle S in

P(theta) and D(pi/2+theta) are two points on the ellipse x^2/a^2+y^2/b^2=1 . Show that the locus of the point of intersection of tangents at P and Q to the ellipse is x^2/a^2+y^2/b^2=2

If P, Q, R are 3 points on a line and Q lies between P and R, then prove that PQ=PR+RQ

In a right triangle ABC, a circle with a side AB diameter is drawn to intersect the hypotenuse AC in P. Prove that the tangent to the circle at P bisects the side BC.

PQ is a chord of length 8 cm of a circle of radius 5 cm. The tangents at P and Q intersect at a point T (see figure). Find the length of TP.

Circles with radii 3,4,5 are touching each other externally , If P is the point of intersection of tangents to these circles at their point of contact ,the distances of P from the points of contact is

The length of a tangent to a circle from a point P is 12 cm and the radius of the circle is 5 cm , then the distance from point P to the centre of the circle is …..

Centre of a circle Q is on the Y-axis. The circle passes through the points (0, 7) and (0, -1). If it intersects the positive X-axis at (P, 0), what is the value of ‘P’?