Manas has drawn a circle with centre O of which AB is a chord. A tangent is drawn at the point B which intersects extended AO at the point. T. If `angle BAT=21^(@),` find the value of `angle BTA.`

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.

Two tangents drawn at the point A and B on a circle intersect each other at the point P. If angle APB=60^(@), then anglePAB=

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.

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=

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.

QR is a chord of the circle with centre O. Two tangents drawn at eh points Q and R intersect each other at the point P. If QM is a diameter, prove that angle QPR=2 angleRQM[GP-X]

O is the centre of the circle and two tangents are drawn from a point P to this circle at points A and B. If angleAOP=50^(@) , then what is the value (in degrees) of angleAPB ?

In the figure given below (not drawn to scale), A, B and C are three points on a circle with centre O. The chord BA is extended to a point T such that CT becomes a tangent to the circle at point C. If angle ATC = 30^(@) and angle ACT = 50^(@) , then the angle angle BOA is :

The tangent at a point A of a circle with centre O intersects the diameter PQ of the circle (when extended) at the point B. If angle BAP = 125^(@) , then angleAQP is equal to :

AB is diameter of a circle with centre 'O'. CD is a chord which is equal to the radius of the circle. AC and BD are extended so that they intersect each other at point P. Then find the value of angleAPB .