1. Two chords of length a unit and b unit of a circle make angles 60° and 90° at the centre of a circle respectively, then the correct relation is
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By: anil on 05 May 2019 01.51 am
Length of chord CD = $$a$$ and AB = $$b$$ Let radius of the circle be $$r$$ In $$ riangle$$OAB, by using Pythagoras theorem => $$r^2 + r^2 = b^2$$ => $$2r^2 = b^2$$ => $$r = frac{b}{sqrt{2}}$$ ------Eqn(1) Now, in $$ riangle$$COD, OC = OD = radii => $$angle$$OCD = $$angle$$ODC = $$angle$$COD = 60° => OCD is equilateral triangle => $$a = r$$ ---------Eqn(2) From eqns(1) & (2), we get : $$a = frac{b}{sqrt{2}}$$ => $$b = sqrt{2}a$$
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