A chord is at a distance of 8 cm from the centre of a circle of radius 17 cm. The length of the chord is


Given radius(AO) = 17cm


Length of the chord (AB) = x


distance of the chord from the centre is 8cm.


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


AC = BC


Now in ∆ AOC


Using Pythagoras theorem


AO2 = AC2 + OC2


172 = AC2 + 82


AC2 = 172 – 82


AC2 = 289 – 64


AC2 = 225


AC = 15cm


BC = 15cm


The length of the chord is AC + BC = 15 + 15 = 30 cm.

2