If `P and Qa be a pair of conjugate points with respect to a circle `S`. Prove that the circle on `PQ` as diameter cuts the circle `S` orthogonally.

If P and Q a be a pair of conjugate points with respect to a circle S . Prove that the circle on PQ as diameter cuts the circle S orthogonally.

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

Prove that the diameter is the greatest chord in a circle.

Prove that the diameter is the greatest chord in a circle.

The tangent at a point P on an ellipse intersects the major axis at T ,a n dN is the foot of the perpendicular from P to the same axis. Show that the circle drawn on N T as diameter intersects the auxiliary circle orthogonally.

The tangent at a point P on an ellipse intersects the major axis at T ,a n dN is the foot of the perpendicular from P to the same axis. Show that the circle drawn on N T as diameter intersects the auxiliary circle orthogonally.

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.

Prove that the tangents drawn at the ends of a diameter of a circle are parallel.

Prove that the tangents drawn at the ends of a diameter of a circle are parallel.

Prove that the tangents drawn at the ends of a diameter of a circle are parallel.