Question

The length of the chord of a circle, of radius 13 cm, at a distance of 5 cm from the centre is _________.
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Answer 1

Answer:

Using Pythagoras theorem

(B)^2=(H)^2-(P)^2

(B)^2=(13)^2-(5)^2

(B)^2=169-25

(B)^2=144

B=12

length of chord=2B

therefore length of chord is 2×12=24cm

Answer 2

Answer:

Let AB be a chord of a circle with centre O and radius 13 cm. Draw OL⊥AB. Join OA.

Here, OL=5 cm,OA=13 cm.

In right triangle OLA,

OA2=OL2+AL2

132=52+AL2

AL2=144

AL=12

Since the perpendicular from the centre to a chord bisects the chord. Therefore,

AB=2AL=2×12=24 cm