Math, asked by utsav38, 1 year ago

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

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Answers

Answered by adashinobenio88
9

P be the mid point of AB, So

AP = PB

OP = 12 cm = distance of chord from center
And

AO = 13 cm = Radius

Now, OPA forms a right angle triangle.
Now, by pythagorous theorem,

AO2 = OP2 + AP2

AP2 = AO2 - OP2

AP2 = 132 - 122

AP2 = 169 - 144

AP2 = 25

AP = 5 cm.
Now,

AB = AP + PB = AP + AP = 5 +5 = 10 cm.
Hope it helps! ^^

Answered by Brenquoler
358

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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