PR is a diameter of a circle. A tangent is draewn at the point P and a point S is taken on the tangent of the circle is such a way that PR=PS. If RS intersects the circle at the point T., prove that ST =PT.

P is any point on diameter of a circle with centre O.A perpendicular drawn on diameter at the point O intersects the point O intersects the circle at the point Q. Extended QP intersects the circle at the point R.A tangent drawn at the point R intersects extended OP at the point S. Prove theat SP=SR. [GP-X]

TA and TB are tangents to a circle with centre O from an external point T. OT intersects the circle at point P. Prove that AP bisects the angle TAB.

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

Three points P,Q ,R lie on a circle. The two perpendiculars PQ and PR and the point P intersect the circle at the points S and T respectively. Prove that RQ=ST

In figure if PR is tangent to the circle at P and O is the centre of the circle then angle POQ is

AB is a diameter of a circle with centre O , P is any point on the circle, the tangent drawn through the point P intersects the two tangents drawn through the points A and B at the points Q and R respectively. If the radius of the circle be r , then prove that PQ.PR=r^(2) .

Two circles intersect at two points P and S.QR is a tangent to the two circles at Q and R. If /_QSR=72^(@), then /_QPR=.

Tangents to a circle at points P and Q on the circle intersect at a point R. If PQ= 6 and PR= 5 then the radius of the circle is