`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)`.

PQ is a diameter. The tangent drawn at the point R, intersects the two tangents drawn at the points P and Q at the points A and B respectively. Prove that angle AOB is a right angle.

OA is the radius of a circle with centre at Q, AQ is its chrod and C is any point on the circle. A circle passes through the point O,A,C intesect the chrod AQ at the point P. Prove that CP=PQ

Write True or False P is any point inside the circle. The tangent to the circle always passes through the point P.

AB is a diameter of the circle with centre at O. R is any point on the circumference of the circle. If /_ ROA = 120^@ , then firnd the volue of /_RBO /

PQ is a diameter of the circle with centre at O. The tengent drawn at A on the circle intersect the extended PQ at R. If angle PRA=45^(@), then angle OAP=

In the figure, O is the centre and BOA is a diameter of the circle. A tangent drawn to the circels at the point P intersects the extended BA at the point T. If angle PBO=30^(@), find the value of angle PAT.

The tangents are drawn at the extremities of diameter AB of a circle with centre P. If a tangent to the circle at the point C intersects the other two tangents at Q and R, thenthe measure of the angleQPR is___

In the adjoining figure, two tangents drawn from external point C to a circle with centre O touches the circel at the point P and Q respectively. A tangent drawn at another point R of the circle intersects CP and CQ at the points A and B respectively. If CP = 7 cm and BC =11 cm, then determine the length of BR.

AB is a diameter of a circle with centre O . A line drawn through the point A intersects the circle at the point C and the tangent through B at the point D . Prove that (a) BD^(2)=AD.DC . (b) The area of the rectangle of formed by AC and AD for any straight line is always equal.