Question

Find the length of a chord which is at a distance of 5cm from the Centre of a circle of radius 13 cm

Answer 1

Answer:

Step-by-step explanation:

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  =5 2  +AL2

AL2  =144

AL=12

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

AB=2AL=2×12=24 cm

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Answer 2

Step-by-step explanation:

Let AB be the chord of a circle of radius 13 cm at a distance of 5cm from centre O.

Then, OA=13xm, OM=5cm

Using Pythagoras theorem,

OA²=OM²+AM²

i.e.,.

${13}^{2} = {5}^{2} + {am}^{2}$

or

${AM}^{2} = {13}^{2} - {5}^{2}$

$= 169 - 25 = 144$

$AM = 12$

$AB = 2 \times 12 = 24cm$

perpendicular perpendicular from centre bisector of chord

length of the chord = 24 cm