In the given figure, A, B, C and D are four points on a circle. AC and BD intersect at a point E such that `angle BEC = 130^(@) and angle ECD = 20^(@). ` . Find `angle BAC.`

In the given figure, A, B and C are three points on a circle with centre O such that angle BOC = 30 ^(@) and angle AOB = 60^(@). If D is a point on the circle other than the are ABC, find angle ADC.

In cyclic quadrilateral ABCD. Diagonals AC and BD intersect at P. If angle DBC = 70^(@) and angle BAC = 30^(@) , find angle BCD.

In the given figure ABCD is a cyclic quadrilateral in which AC and BD are its diagonals. If angle DBC = 55 ^(@) and angle BAC = 45 ^(@), find angle BCD.

In the given figure, angle PQR = 100^(@), where P, 9 and R are points on a circle with centre O. Find angle OPR.

In the given figure. If TP and TQ are the two tangents to a circle with centre O so that angle POQ= 110^(@) , then angle PTQ is equal to …….

In the given figure, A, B and C are points on OP, OQ and OR respectively such that AB||PQ" and "AC||PR . Show that BC||QR .

In the given figure, angle BCD = 43 ^(@) and angle BAE = 62 ^(@). Find the values of a,b,c and d.

In the given figure, AB is a diameter of the circle, CD is chord equal to the radius of the circle, AC and BD when extended intersect at a point E. Prove that angle AEB = 60^(@).

ABCD is a cyclic quadrilateral whose diagonals intersect at a point E. If angle DBC = 70^(@), angle BAC is 30^(@), find angle BCD. Further, if AB = BC, find angle ECD.

In the given figure, AC = AE, AB = AD and angle BAD = angle EAC . Show that BC = DE.