Q4 of 31 Page 65

The lengths of two chords of a circle with its centre O are 6 cm. and 8 cm. If the distance of smaller chord from centre is 4 cm, then let us write by calculating, the distance of other chord from the centre.


Let Smaller Chord is EF, the other chord is BC, distance from the centre o to smaller chord is OG.


⇒ BC = 8cm


⇒ CD


Perpendicular from the center of the circle to any Chord bisects it in two line segments



⇒ CD = 4cm


⇒ EF = 6cm


⇒ EG


⇒ EG = 3cm


⇒ OG = 4cm


In OEG, Using Pythagoras Theorem


⇒ OE2 = OG2 + EG2


⇒ OE2 = 16 + 9


⇒ OE2 = 25


⇒ OE = 5cm


In OCD,Using Pythagoras Theorem


⇒ OC2 = CD2 + OD2


⇒ 52 = 42 + OD2


⇒ 25 = 16 + OD2


⇒ OD2 = 9


⇒ OD = 3cm


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