What is the distance in cm between two parallel chords of lengths 32 cm and 24 cm in a circle of radius 20 cm?
Explanation:
The two chords AB and CD can be on the same side or the opposite sides of the centre O.
Let M and N be the midpoints of AB and CD. ∴ MN is the distance between the two chords.
MB = 12 cm and ND = 16 cm
OM and ON are perpendicular to AB and CD respectively.
ON2 = OD2 - ND2 (By Pythagoras theorem) ⇒ ON2 = 202 – 162 ⇒ ON = 12 cm
Similarly,OM2 = OB2 - MB2 ⇒ OM = 16 cm
Case 1: AB and BC are on the same side of the centre. MN = OM – ON = 4 cm
Case 2: AB and BC are on opposite sides of the centre. MN = OM + ON = 28 cm
Hence, option (d).
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