In the given figure below, two chords of lengths x metre and y metre subtend angles 60∘ and 90∘ at the centre of the circle respectively. Which of the following is true?

(a): Radius of circle = r units In ΔOCD,∠COD=90∘ ∴CD2=OC2+OD2 ⇒y2=r2+r2=2r2       .,..(i) In ΔOAB, OE⊥AB ∠OAB=60∘ AE=x2 ∴cos60∘=AEOA ⇒12=x2r ⇒12=x2r⇒x=r            ??(ii) From equations (i) and (ii), y2=2x2