Find the length of a chord which is at a distance of 9 cm from the centre of a circle of radius 15 cm.


Given radius(AO) = 15cm


Length of the chord (AB) = x


distance of the chord from the centre is 9cm.


Draw a perpendicular bisector from center to the chord and name it OC.


AC = BC


Now in ∆ AOC


Using Pythagoras theorem


AO2 = AC2 + OC2


152 = AC2 + 92


AC2 = 152 – 92


AC2 = 225 – 81


AC2 = 144


AC = 12cm


BC = 12cm


The length of the chord is AC + BC = 12 + 12 = 24 cm.


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