Question

If a chord a length 8 cm is situated at a distance of 3 cm form centre, find the diameter of circle​

Answer 1

Given,

For any circle a 8 cm long chord is situated just 3 cm from the center.

To find,

The diameter of the circle using formula.

Solution,

To solve this we can use the following mathematical process.

First, assume the name of the chord, the center, and the radius of the circle. And then apply Pythagoras theorem ,which is,

The square of the hypotenuse is equal to the sum of the squares of the other two sides of a triangle

Assume that AM is the chord with length of 8 cm.

The center is at point O.

Now assume that the middle point of the chord is B. So AB=BM=$\frac{8}{2}$=4cm .

The distance of the chord from the center is OB is 3 cm.

We know OB⊥AM. As OB is the shortest distance.

So if we connect the points O and A we get OA, which will be the radius of the circle.

By pythagoras theorem in ΔOBA , AB²+OB²=OA².

⇒4²+3²=OA².

⇒OA²=25.

⇒OA=5.

Thus ,

The radius of the circle,OA is 5cm.

So the diameter will be 2×OA=2×5=10cm.

Hence, The diameter of the circle is 10cm.