Question

Area and Circumference of Circles

Answer 1

Pi($\pi$) is the ratio of circumference to diameter for any circle.

Perimeter is the distance around a circle.

Circumference of circle $C = \pi d$.

Perimeter of circle $= 2 \pi r$

What is circle ?

A circle is a spherical shape without boundaries or edges.

A circle is a closed, curved object with two dimensions in geometry.

Consider two small arcs AB and CD of two circles of radii x and y units, both of which make an angle of measure θ at the centers P and Q respectively.

For smaller values of θ, the arc length AB is almost equal to the length of the line segment $\bar{AB}$. Similarly, arc CD ≅ $\bar{CD}$.

Using the SAS rule of triangle similarity, we can say that APB and CQD are similar triangles because their angles are the same and their ratios are AP: PB = CQ: QD = 1: 1. So, it stands to reason that AB: AP = CD: CQ.

Circumference = $\pi \times$ diameter or circumference = 2$\pi \times$ radius if this constant equals some value.

So it was proved.

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