Question

(1) The radius of a circle is 5 cm. The distance of a chord from the centre is 4 cm. Find the length of the chord.
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Answer 1

here is your answer..

Answer 2

Given,

The radius of a circle = 5 cm

The distance of the chord from the center = 4 cm

To find,

The length of the chord.

Solution,

We can simply solve this mathematical problem using the following process:

Let us assume that the length of the chord is x cm.

Geometrically,

The distance of a chord from the center of a circle refers to the distance between the midpoint of the chord and the center of the circle.

This implies half of the chord, the line joining the midpoint of the chord with the center, and the radius of the circle form a right-angled triangle. The radius of the circle forms the hypotenuse.{Statement-1}

Now, according to the question and statement-1;

On applying the Pythagoras theorem, we get;

(length of the chord/2)^2 + (distance between the midpoint of the chord and the center of the circle)^2 = (radius of the circle)^2

=> (x/2)^2 + (4 cm)^2 = (5 cm)^2

=> (x/2)^2 = (5 cm)^2 - (4 cm)^2 = (25-16) cm^2 = 9 cm^2

=> (x/2)^2 =(3 cm)^2

=> x/2 = 3 cm

=> x = 6 cm

=> length of the chord = 6 cm

Hence, the length of the chord is equal to 6 cm.