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`.

PQ is a diameter of the circle with centre at O. The tangent drawn at C on the circle intersects externded PQ at R. If angle CPO =30^(@), then find the value of angle QCR.

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

Two radii OA and OB of a circle with centre O are perpendicular to each other. If two tangents are drawn at the point A and B intersect each other at the point T, prove that AB= OT and they bisect each other at a ridght angle.

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) .

AB is a chord of a circle with centre at O and radius 13 cm in length If AB = 10cm then find the distance from centre to the chord.

Choose the correct answer and give justification for each. In the figure XY and X^(1)Y^(1) are two parallel tangents to a circle with centre O and another tangent AB with point of contact C intersecting XY at A and X^(1)Y^(1) at B then /_AOB=

XY and X'Y' are two parallel tangents to the circle with centre at O. Antoher tangent AB touches the circle at C and XY at A and X'Y' at B. Prove that angleAOB=90^(@) .

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 adjacent figure, AB be diameter of a circle whose centre is O. If angleAOE = 150^@ , angleDAO =51^@ then the measure of angleCBE is___