Question 3 The lengths of two parallel chords of a circle are 6 cm and 8 cm. If the smaller chord is at distance 4 cm from the centre, what is the distance of the other chord from the centre?
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Solution
Let AB and CD be two parallel chords in a circle centered at O. Join OB and OD. Given, AB = 6 cm and CD = 8 cm Distance of smaller chord AB from the centre of the circle is 4 cm i.e; OM = 4 cm MB=AB2=62=3cm (Perpendicular from the centre bisects the chord)
In ΔOMB OM2+MB2=OB2 (4)2+(3)2=OB2 16+9=OB2 OB=√25 OB=5cm
In ΔOND, OD =OB=5cm (Radii of the same circle) ND=CD2=82=4cm ON2+ND2=OD2 ON2+(4)2=(5)2 ON2=25−16=9 ON=3 Therefore, the distance of the bigger chord from the centre is 3 cm.