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°

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

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.

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°

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.

AOB is a diameter of a circle whose center is O. The point C lies on the circle. If ∠OBC = 60°, find the value of ∠OCA.

If A = , then A² is equal to: (a) (b) (c) (d)

Statement 1: The point which is equidistant from three non-collinear points D, E and F is the circumcentre of △DEF. Statement 2: The incentre of a triangle is the point where the bisectors of the angles intersect. (a) Both statements are true. (b) Both statements are false. (c) Statement 1 is true and Statement 2 is false. (d) Statement 1 is false and Statement 2 is true.

Mr Anuj deposits ₹500 per month for 18 months in a recurring deposit account at a certain rate. If he earns ₹570 as interest at the time of maturity, then his matured amount is: (a) ₹(500 × 18 + 570) (b) ₹(500 × 19 + 570) (c) ₹(500 × 18 × 19 + 570) (d) ₹(500 × 9 × 19 + 570)