Let ‘O’ be the centre of a circle, PQ is a diameter, then prove that `angle PRQ = 90^@` (OR) Prove that angle in a semi-circle is right angle.

Find the area of a sector of a circle whose diameter is 28cm and central angle is 120^@

In the Fig, 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

Prove that the tangents to a circle at the end points of a diameter are parallel.

If angle A and angle P are acute angles such that sin A =sin P then prove that angle A =angle P

The area of a sector of a circle 1/20 the area of the circle Find the sector angle.

In a right-triangle ABC in which angleB=90^(@) , a circle is drawn with AB as diameter intersecting the hypotenuse AC at P. Prove that the tangent to the circle at P bisects BC.

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

Let A, B be the centres of two circles of equal radii, draw them so that each one of them passes throught the centre of the other. Let them intersect at C and D. Examine whether AB and CD are at right angles.