In a circle O and of radius 13 cm, two parallel chords are drawn on different sides of the centre. If the length of one chord is 10 cm and the distance between the two chords is 17cm, then find the difference in lengths of the two chords (in cm).
Show answer & explanation
Correct answer: D
Explanation
The correct answer is option 4 i.e. 14
Perpendicular from the center bisects the chord.
AQ = 5 cm
By Pythagoras theorem,
OA = (OQ2 - AQ2)1/2 = (169 - 25)1/2 = (144)1/2 = 12 cm
OB = AB - OA = 17 - 12 = 5 cm
BS = (OS2 - OB2)1/2 = (169 - 25)1/2 = (144)1/2 = 12 cm
Length of the other chord = 24 cm
Differnce between the length of the two chords = 24 - 10 = 14