(i) Define a sector of a circle. (ii) Two sectors are cut from the SAME circle and…
MATHEMATICS · Subjective · CBSE · Mathematics · Areas Related to Circles · Areas Related to Circles
Problem
(i) Define a sector of a circle.
(ii) Two sectors are cut from the SAME circle and have central angles θ1 and θ2. Prove, without using numerical substitution, that
Area of sector 2Area of sector 1=θ2θ1.
(iii) A student claims that the statement in part (ii) holds even when the two sectors are taken from two DIFFERENT circles. Give a clear explanation, with reasons, to show whether the student’s claim is always true, sometimes true, or never true.