Question

the radius of a circle with Centre O is 13 cm the distance of a chord from centre is 5 find the length of the chord​

Answer 1

Answer:

Length of chord = 24 cm

Step-by-step explanation:

Radius = 13 cm

Distance of chord from center = 5 cm.

This distance is perpendicular and will divide the chord into 2 equal parts. Let the length of each equal part be x. So the length of the chord will be 2x.

2 right angled triangles are formed, where hypotenuse = 13 cm, side1 = 5cm, side2 = x cm

By applying pythagoras theorem,

hypo² = side1² + side2²

13² = 5² + x²

169 = 25 + x²

x² = 169 - 25

x² = 144

x = 12 cm

Length of chord = 2x

                           = 2(12)

Length of chord = 24 cm

Hope this helps! :)

Answer 2

Answer:

24 cm

Step-by-step explanation:

let the chord be PQ

let OR be perpendicular on PQ which bisects it into two equal partsnin which

PR = PQ                                                    ....................(1)

then we have find that ,

OP = radius = 13 cm

OR = distance from the center to the chord =  5cm

we have also find that OPR is a phythagorus theorum, in which ,

OP^(2) = OR^(2) + PR^(2)

13^2 = 5 ^ 2 + PR^2

169 = 25 + PR^2

169-25 = PR^2

PR^2 = 144

PR = sq.root144 = 12cm

PR = PQ                                                                       ...................using(1)

2PR = PQ = length of the chord

lenght of the chord = 2(12cm) = 24 cm

hope it will help u

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