Q2 of 6 Page 116

Radius of a circle with centre O is 25 cm. Find the distance of a chord from the centre if the length of the chord is 48 cm.


As we know that, the perpendicular from the centre of a circle to a chord bisects the chord.


Therefore, OP perpendicular to CD and OP bisects the CD. Therefore, it makes a right angle triangle, which is ∆OPD. We have OD=25 cm and PD=48/2=24 cm.


By Pythagoras theorem,


OD2 = OP2 + PD2


OP2 = OD2 - PD2


OP2= (25)2 - (24)2


OP2 = 625 – 576


OP2 = 49


OP = 7 cm


Therefore, distance of the chord from the centre is 7 cm.


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