Question

A circle has a radius of 12cm. How do you find the circumference and diameter of the circle? What is the maximum length of any chord of the circle?

Answer 1

Hint: Now we know that the diameter of the circle is twice the radius of the circle. Hence now we have the diameter of the circle. Now the circumference of the circle is given by $2\pi r$ Hence substituting the value of r we can find the circumference of the circle. Now similarly the largest chord of the circle is the chord passing through the center of the circle and hence is the diameter.

Complete step-by-step answer:
Now let us first understand what a circle is?
A circle is a geometrical figure with collection of all points equidistant from a particular point.
This particular point is called the center of the circle.
Now since all the points are equidistant from this centre we can say that the distance of any point on the circle and centre is constant. This constant distance is called radius of circle.
Hence radius is nothing but the distance of any point on the circle from center.
Now the circumference of the circle is the perimeter of the circle. The circumference of the circle is given by $2\pi r$ where $\pi =\dfrac{22}{7}$ approximately.
Now let us understand the meaning of a chord. A chord is a line segment joining any two points on circumference of the circle. Now if the chord passes through the centre then the chord is of largest length and is called the diameter of the circle. The length of diameter is twice the radius of the circle.
Consider the given example.
Hence OP is radius PQ is diameter which is the largest chord and QR is a chord.

Now we are given a circle with the radius of 12cm.
Hence the diameter of the circle is 2 × 12 = 24cm.
Hence the largest chord is of 24cm
Now the circumference of the circle is $2\pi r=2\times \dfrac{22}{7}\times \left( 12 \right)=75.42$

Note: Now note that the number $\pi $ is an irrational number and hence cannot be written in the form of $\dfrac{p}{q}$ . But approximately write $\pi =\dfrac{22}{7}$ or $\pi =3.14$ for calculation purposes. Also note that the area of the circle is given by $\pi {{r}^{2}}$ and the circumference is given by $2\pi r$ or $\pi d$ .