In the adjacent figure lines PQ and RS intersect each other at point O. If `anglePOR : angleROQ `= 5: 7, find all the angles.

In the given figure if line segments PQ and RS intersect at point T, such that anglePRT = 40^(@), angleRPT = 95^(@) and angleTSQ = 75^(@) , find angleSQT

In the adjoining figure, two circles with centres P and Q intersect each other at the points B and C, ACD is a line segment . If angleARS=150^(@)andangleBQC=x^(@) , then find the value of x.

In the given figure lines bar(AB) and bar(CD ) intersect at O. If angleAOC+ angleBOE= 70^(@) and angleBOD = 40^(@) , find angleBOE and reflex angleCOE .

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]

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=

In the adjoining figure , the diagonals of the cyxlic quadrilateral PQRS intersect each other at the point X in such a way that anglePRS=65^(@) andangleROS=45^(@) . Find the values of angleSQP and angleRSP .

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]

Two two circle with their centre at P and Q intersect each other, at the point A and B . Through the point A , a straight line parallel to PQ intersects the two circles at the points C and D respectively . If PQ = 5 cm , then determine the lenght of CD .

In a rectangle figure ABCD, the two diagonals AC and BD intersect each other at the point O, ifAB = 12 cm,AO = 6.5 cm, then the length of BC is "…..........." cm.