Question

The radius of a circle is 13 cm and ab is a chord which is at a distance of 12 cm from the centre then find the length of the chord

Answer 1

r=13cm

a chord is at a distance of 12cm

so to find ab we have draw a hypotenuse to the radius r

then putting the value of Pythagoras theorem we have

(oa^2=po^2+pa^2)+(ob^2=op^2+pb^2)

so ap=√13^2-12^2=√169-144=5

pb=√13^2-12^2=√169-144=5

si the length of ab is ap+pb

5+5=10

hence the length of the chord is 10cm

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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