Question

radius of a circle with O is 41 units.Length of a chord PQ is 80 onits, find the distance of the chord from the centre of the circle

Answer 1

the distance of the chord from the centre of a circle is 9 units

Answer 2

Answer:

Distance of the chord from the centre of the circle = 9 units

Step-by-step explanation:

In the question,

Radius of the circle, r = 41 units

Length of the chord, l = 80 units

Now,

Let us say the distance of the centre of the circle from the chord is = d

So,

As the perpendicular drawn from the centre of the circle to the chord bisects the chord into two equal parts.

So,

Using the Pythagoras theorem we get,

$r^{2}=d^{2}+(\frac{l}{2})^{2}\\So,\\(41)^{2}=d^{2}+(\frac{80}{2})^{2}\\d^{2}=41^{2}-40^{2}\\d^{2}=81\\d=9\ units$

Therefore, the Distance of the chord from the centre of the circle is given by,

d = 9 units.