Check whether the following statement is true or false. Justify your answer.
If the length of an arc of a circle of radius r is equal to that of an arc of a circle of radius 2r, then the angle of the corresponding sector of the first circle is double the angle of the corresponding sector of the other circle.

Question

Check whether the following statement is true or false. Justify your answer.
If the length of an arc of a circle of radius r is equal to that of an arc of a circle of radius 2r, then the angle of the corresponding sector of the first circle is double the angle of the corresponding sector of the other circle.

KnowledgeBoat · Accepted Answer

We know that, Arc length = × 2πr Let L1 and L2 be the arc length of first circle and second circle and 1 and 2 be the central angle of the sector for the first circle and second circle respectively. Arc length for first circle (L1) = × 2πr Arc length for second circle (L2) = × 2π(2r) L2 = × 4πr According to question : L1 = L2 × 4πr 2 1 = 4 2 1 = 2 2 ∴ Angle of the corresponding sector of the first circle is double the angle of the corresponding sector of the other circle. Hence, the statement is True.

Mathematics

Mensuration

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