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.

Prove by vector method that an angle in a semi-circle is a right angle.

Prove that an angle inscribed in a semi-circle is a right angle using vector method.

If r_1=r_2+r_3+r prove that the triangle is right angled .

O is the centre of the circle QOR is diameter. PQ is tangent to the circle. Given P hat(O)R = 130^(@) . Find O hat(P)Q .

The circular wire of diameter 10 cm is cut and placed along the circumference of a circle of diameter 1 meter. The angle subtended by the wire at the centre of circle is equal to

PQ is a tangent drawn from a point P to a circle with centre O and QOR is a diameter of the circle such that angle POR =120^(@) . Find angle OPQ .

In the adjoining figure seg RS is the dianeter of the circle with centre 'O' . Point T is in the exterior of the circle . Prove that angleRTS is an acute angle.

O is the centre of a circle, angleAOB=100^(@) . Then angle angleACB = . . . . . . . . .

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