AB is the diameter of the circle with centre O. From a point P on the circle, a perpendicular PN is drawn on AB. Prove geometrically that PB² = AB.BN.

Prove that in any circle, angles in the same segment are equal.

What is the value of a semicircular angle?

‘O’ is the center of a circle and PQ is a diameter. R is a point on the circle such that PR = RQ, then the value of ∠RPQ: (a) 30° (b) 90° (c) 60° (d) 45°

State True/False: “The equal chords of a circle are at equal distances from the centre of the circle.”

O is the circumcentre of the triangle ABC. OD ⊥ BC. Prove that ∠BOD = ∠BAC.

AB is a diameter of a circle with centre O. If the chord AC subtends ∠60° at the centre then value of ∠OCB is (a) 20° (b) 30° (c) 40° (d) 50°

The angle in the segment of a circle which is greater than a semicircle is acute or obtuse?

Fill up the blank : The front angle formed at the center of a circle by an arc is the ____ of the angle formed by the same arc at any point on the circle.

Assertion (A): If sin² A + sin A = 1, then cos⁴ A + cos² A = 1. Reason (R): 1 − sin² A = cos² A. (a) A is true, R is false. (b) A is false, R is true. (c) Both A and R are true, and R is the correct reason for A. (d) Both A and R are true, and R is not the correct reason for A.

In the given diagram, chords AC and BC are equal. If ∠ACD = 120°, then ∠AEC is: (a) 30° (b) 60° (c) 90° (d) 120°

A man invested in a company paying 12% dividend on its shares. If the percentage return on his investment is 10%, then the shares are: (a) at par (b) below par (c) above par (d) cannot be determined