🌐 All Subjects 🔬 Science 🌍 Social Science 📐 Mathematics 📖 English 🪶 हिन्दी
← Back to Chapter 5 Exercises

⭕ Chapter 5: I'm Up and Down, and Round and Round • Exercise Set 5.6

Verified step-by-step solutions for your class notes.

Exercise Set 5.1 3Think, Draw and Infer 1Exercise Set 5.2 2Exercise Set 5.3 3Exercise Set 5.4 2Exercise Set 5.5 3Exercise Set 5.6 1End-of-Chapter Exercises 12All Exercises 27
Q1

In a circle with centre O, the central angle AOB is $60^\circ$. If the radius of the circle is 12 cm, what is the length of the chord AB?

Answer: In $\Delta AOB$, $OA = OB = 12\text{ cm}$ (radii). This makes it an isosceles triangle, so $\angle OAB = \angle OBA$. Since $\angle AOB = 60^\circ$, the other two angles must also be $(180^\circ - 60^\circ) / 2 = 60^\circ$. Because all three angles are $60^\circ$, $\Delta AOB$ is an equilateral triangle. Therefore, the chord $AB$ is equal in length to the radii, so $AB = \mathbf{12\text{ cm}}$.

O (60°) A B 12 cm 12 cm AB = 12 cm
Equilateral ΔAOB: OA = OB = AB = 12 cm