Question

4. Radius of circle is 10 cm. There are two chords of length 16 cm. each. What will be the distance of these chords from the center of the circle ? ​

Answer 1

Given,

Radius of circle (r) = 10cm

Length of a chord (l) = 16 cm

To Find,

Distance of chord from circle's center

Solution,

We first notice from the information given in the question that the radius is 10 cm and let us name the center of the circle as 0.

Let us consider a chord AB that lies on one side of the circle of length 16cm.

Now drop a perpendicular from the center of the circle to this chord.

Using the theorem that "A line from the center of the circle and perpendicular to the chord divides the chord into two halves"

we will move forward.

Let the point of fall of the perpendicular to the chord be M.

So you can see a right-angled triangle been formed ∧ AOM

where the hypotenuse is OA also the radius of the circle which is 10cm

The base of the triangle is AM which is 8cm (using the theorem $16/2$ )

Let OM be $x$ cm

Using the Pythagorean theorem,

$10^{2} = 8^{2} + x^{2}$

$100=64+x^{2} \\100-64=x^{2} \\36=x^{2} \\\sqrt{36}=x\\6= x$

Hence the distance of these chords from the center of the circle is 6 cm each.