In a circle of radius 17 cm, two parallel chords are drawn on opposite side of a diameter. The distance between the chords is 23 cm. If the length of one chord is 16 cm, then the length of the other is

Given that,

AB || CD (Chords on opposite side of centre)


DO = BO (Radii)


OL and OM perpendicular bisector of CD and AB respectively


LM = 23 cm


AB = 16 cm


In OLB,


OB2 = OL2 + LB2


OL2 = 225


OL = 15 cm


OM = LM - OL


= 8 cm


In OMD,


OD2 = OM2 + MD2


MD2 = 225


MD = 15 cm


Now,


CD = 2 MD = 30 cm

22