Radius of a circle is 10 cm. Angle made by chord AB at the centre of this circle is 60 degree. What is the length of this chord?

Question

Question

This question was previously asked in

SSC CGL 2022 Tier-I Official Paper (Held On : 01 Dec 2022 Shift 1)

Answer 1

Given:

The radius of a circle is 10 cm. The angle made by chord AB at the center of this circle is 60 degrees.

Concept used:

1. In an Isosceles triangle, the two angles opposite to the equal sides are equal to each other.

2. In an equilateral triangle, since the three sides are equal therefore the three angles, opposite to the equal sides, are equal in measure.

Calculation:

F2 Savita SSC 1-2-23 D2

OA = OB = 10 cm

ΔOAB is an isosceles triangle.

So, ∠OAB = ∠OBA = \(\frac {(180 - 60)^\circ}{2}\) = 60°

Since ∠OAB = ∠OBA = ∠AOB = 60°, ΔOAB is an equilateral triangle.

So, OA = OB = AB = 10 cm

∴ The length of this chord is 10 cm.

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