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Question
In a circle of radius 10 cm, AB and CD are two parallel chords of lengths 16 cm and 12 cm respectively.
Calculate the distance between the chords, if they are on:
(i) the same side of the center.
(ii) the opposite sides of the center.
Solution
Given that AB = 16 cm and CD = 12 cm
So, AL = 8 cm and CM = 6 cm ....( ⊥ from the center to the chord bisects the chord )
In right triangle OLA and OMC,
By Pythagoras theorem,
OA2 = OL2 + AL2 and OC2 = OM2 + Cm2
102 = OL2 + 82 and 102 = OM2 + 62
OL2 = 100 - 64 and OM2 = 64
OL2 = 6 cm and OM2 = 8 cm
(i) In the first case, distance between AB and CD is
LM= OM - OL = 8 - 6 = 2 cm
(ii) In the second case , distance between AB and CD is
LM = OM + OL = 8 + 6 = 14 cm
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