Two tangents to a circle at A and B intersect at a point P. If `angleAPB = 68^@` then find `anglePAB`.

Two tangetns from A and B which are lie on the circle intersect at the point P. If angleAPB = 68^@ then find the measurement of anglePAB .

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=

Two diagonals AC and BD of a cyclic quadrilateral ABCD intersect at P. If angleAPB = 68^@ and angleCBD =24^@ , then angleADB =

P and Q are two points ona circle with centre at O. R is a point on the minor arc of the circle, between the points P and Q. The tangents to the circle at the points P and Q meet each other at the points S. If anglePSQ =20^@ , then anglePRQ =

Two circles touch each other externally at P. AB is a direct common tangent to the circles, A and B are point of contact and anglePAB =35^@ . Then angleABP is___

In the adjoining figure , two circles intersect each other at the points P and Q. If angleQAD=80^(@)andanglePDA=84^(@) , then find the value of angleQBCandangleBCP

Two chords AC and BD of a circle intersect each other at the point O. If two tangents drawn at the points A and B intersect each other at the point P and two tangents drawn at the points C and D intersect at the point Q, prove that angle P+ angle Q =2 angle BOC. [GP-X]

The centre of two circle are P and Q they intersect at the points A and B. The straight line parallel to the line segment PQ through the point A intersects the two circles at the point C and D Prove that CD = 2PQ

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.

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]