Question

Assertion: In the circle with centre O, AB = 18 cm, OA = 15 cm and ON ⊥ AB. ∴ MN = 3 cm

Reason: Perpendicular from the centre to a chord bisects the chord.

Options

• Both A and R are true and R is the correct reason for A.

• Both A and R are true but R is the incorrect reason for A.

• A is true but R is false.

• A is false but R is true.

Answer 1

Both A and R are true and R is the correct reason for A.

Explanation:

Given, in the circle with centre O, AB = 18 cm, OA = 15 cm, and ON is perpendicular to AB. According to the theorem, the perpendicular drawn from the centre of a circle to a chord bisects the chord. Therefore, OM = MB = 9 cm. Using the right triangle OMB, we calculate ON (distance from centre to chord) and then find the difference for MN as 3 cm.

Thus, the statement “MN = 3 cm” is true because the perpendicular from the centre to the chord bisects the chord.