Q4 of 6 Page 116

C is the centre of the circle whose radius is 10 cm. Find the distance of the chord from the centre if the length of the chord is 12 cm.


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


So here we have C as a centre where CP is perpendicular on AB which bisects the chord AB and radius as CA = 10 cm and chord length = 12 cm, so AP=6cm.


It makes a right angle triangle ∆CPA.


Therefore, by using Pythagoras theorem, we have,


AC2 = CP2 + AP2


We have to find CP so


CP2 = AC2 - AP2


CP2 = (10)2 – (6)2


CP2 = 100 – 36


CP2= 64


CP = 8 cm


Therefore, a distance of the chord from the centre is 8 cm.


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