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 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 bisectors of angleBand angleC intersect each other in point X. Line AX intersects side BC in point Y. AB=5, AC=4, BC=6 "then find" (AX)/(XY) .

In the given figure lines bar(XY) and bar(MN) intersect at O. If ∠POY = 90^(@) and a: b = 2 : 3, find c.

In the adjacent figure, AB || CD, ‘t’ is a transversal intersecting E and F respectively. If ∠2 : ∠1 = 5 : 4, find the measure of each marked angles.

In the adjoining figure, two circles intersect each other at points M and N . Secants drawn from points M and N intersect cirecls at point R, S, P and Q as shown in the figure.

In the adjoining figure, two circles intersect each other at points A and E . Their common secant through E intersects the circle at points B and D . The tangents of the circles at point B and D intersect each other at point C . Prove that squareABCD is cyclic .

In the adjacent figure ray OS stands on a line PQ. Ray OR and ray OT are angle bisectors of anglePOS and angleSOQ respectively. Find angleROT .

Diagonals of a trapezium ABCD with AB || DC, intersect each other at the point ‘O’. If AB = 2CD, find the ratio of areas of triangles AOB and COD.