In a circle with centre O, the central angle AOB is 60°. If the radius of the circle is 12 cm Class 9

In a circle with centre O, the central angle AOB is 60°. If the radius of the circle is 12 cm Class 9

Question 1.

In a circle with centre O, the central angle AOB is 60°. If the radius of the circle is 12 cm, what is the length of the chord AB? Class 9

Answer:

Let AB be a chord of a circle with centre O.

OA = OB = radius = 12 cm

Given: ∠AOB = 60°

In ∆AOB,

AO = BO = 12 cm

∴ ∠OAB = ∠OBA ... (i) [Angles opposite to equal sides are equal]

In ∆OAB,

∠OAB + ∠OBA + ∠AOB = 180°

∴ ∠OAB + ∠OAB + 60° = 180° ...[From(i)]

∴ 2∠OAB = 120°

∴ ∠OAB = 60°

From (i), ZOBA = 60°

∴ ∆AOB is an equilateral triangle.

∴ Chord AB = 12 cm