Answer :
Pi([tex]\pi[/tex]) is the ratio of circumference to diameter for any circle.
Perimeter is the distance around a circle.
Circumference of circle [tex]C = \pi d[/tex].
Perimeter of circle [tex]= 2 \pi r[/tex]
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 [tex]\bar{AB}[/tex]. Similarly, arc CD ≅ [tex]\bar{CD}[/tex].
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 = [tex]\pi \times[/tex] diameter or circumference = 2[tex]\pi \times[/tex] radius if this constant equals some value.
So it was proved.
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