Question

The length (in cm) of a chord of a circle of radius 13 cm at a distance of 12 cm from its centre is

Answer 1

radius of the circle is 13cm

Distance Is 12cm which is the length of the perpendicular drawn from the centre to the chord.

Therefore,

By Pythagoras theorem

(Half of chord)squared=(13)squared-(12)squared

Half of chord =5cm

Chord =5*2=10cm

Half of chord Is being taken because the perpendicular drawn from centre to the chord bisects it

Answer 2

AB is chord of a circle with center O and OA is its radius OM ⊥ AB

Therefore, OA = 13 cm, OM = 12 cm

Now from right angled triangle OAM,

OA2 = OM2 + AM2 by using Pythagoras theorem,

132 = 122 + AM2

AM2 = 132 – 122

AM2 = 169 – 144

AM2 = 25

AM = 52

We know that OM perpendicular to AB

Therefore, M is the midpoint of AB

AB = 2 AM

AB = 2 (5)

AB = 10 cm

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