In Fig. 12.36 A, B and C are three points on a circle with centre O such that `BOC=30^@ and AOB = 60^@`. If D is a point on the circle other than the arc ABC, find ADC.

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 arc ABC, find angle ADC .

In Fig, A, B, C and D are four points on a circle AC and BD intersect at a point E such that BEC=130^@ and ECD=20^@ . Find BAC.

In the given figure, AP and BP are tangents to a circle with centre O such that AP=5 cm and |__APB=60^(@) . Find the length of chord AB.

If A and B are two points of a circle of radius r with centre at the point O and angleAOB = theta (in radians) then the area of the sector AOB is

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

In the figure, PQL and PRM are tangents to the circle with centre O at the points Q and R respectively and S is a point on the circle such that |__SQL=50^(@) and |__SRM=60^(@) . Find |__QSR .

In the given figure, AD is a diameter of a circle with centre O and AB is a tangent at A. C is a point on the circle such that DC produced intersects the tangent at B and |__ABD=50^(@) . Find |__COA .

Find the length of the tanget to a circle with centre 'O' and radius =6cm from a point P such that OP=10cm .

In the given figure, AB is a chord of a circle with centre O such that AB=16cm and radius of the circle is 10 cm. Tangent at A and B intersect each other at P. Find PA.

In the given fig OACB is a quadrnat of a circle with centre O and radius 3.5 cm . If OD = 2cm find the area of the shadded region .