Through a point A on a circle, a chord AP is drawn & on the tangent at A a point T is taken such that `AT = AP`. If TP produced meet the diameter through A at Q, prove that the limiting value of AQ when P moves upto A is double the diameter of the circle.

Through a point A on a circle,a chord AP is drawn & on the tangent at A a point T is taken such that AT=AP. If TP produced meet the diameter through A at Q,produced meet the limiting value of AQ when P moves upto A is double the diameter of the circle.

If the diameter through any point P of a parabola meets any chord in A and the tangent at the end of the chord meets the diameter in B and C, then prove that PA^(2)=PB.PC

The tangents drawn at the end points of the diameter of a circle will be

AP is tangent to circle O at point P, What is the length of OP?

The tangent at any point P of a circle x^(2)+y^(2)=a^(2) meets the tangent at a fixed point A(a,0) in T and T is joined to B ,the other end of the diameter through A ,prove that the locus of the intersection of AP and BT is an ellipse whose eccentricity is (1)/(sqrt(2))

Prove that a diameter AB of a circle bisects all those chords which are parallel to the tangent at the point A.

Draw the tangent to a circle of diameter 4 cm at a point P on it.