A pair of tangents are drawn to a unit circle with centre at the origin and these tangents intersect at A enclosing an angle of `60^0`. The area enclosed by these tangents and the arc of the circle is

OA and OB are the radius of a circle with centre at O and angleAOB= 150^@ . The tangents at A and B intersects at C. Find angleACB .

Tangents are drawn to the hyperbola 4x^2-y^2=36 at the points P and Q. If these tangents intersect at the point T(0,3) then the area (in sq units) of triangle PTQ 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.

If y= 3x is a tangent to a circle with centre (1, 1) , then the other tangent drawn throught (0, 0) to the circle is-

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___

If the tangents are drawn to the circle x^2+y^2=12 at the point where it meets the circle x^2+y^2-5x+3y-2=0, then find the point of intersection of these tangents.

A pair of tangents are drawn from the origin to the circle x^2+y^2+20(x+y)+20=0 . Then find its equations.

Prove that if two tangents are drawn to a circle from a point outside it, then the line segments joining the point of contact and the exterior point are equal and they subtend equal angles at the centre.

If two tangents are drawn to a circle from a point outside it, then the line segment joining the point of contact and the exterior point are equal and they subtend equal angles at the centre.

From a point P, two tangents PA and PB are drawn to a circle with centre O. If OP is equal to diameter of the circle then angleAPB is___