Question

find the length of chord of Chord which is at distance of 12 cm from the centre of a circle of radius 13 cm​

Answer 1

Answer:

use pythogoras theorem ,

we know , perpendicular drawn from the center of the circle to the chord bisects the chord .

then , √(13)² -  (12)² = half the length of chord

half the length of chord =  √169-144

                                        = √25

                                       = 5 cm

then the length of the chord = 5 x 2

                                                = 10 cm

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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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