Question

A 2 cm by 4 cm rectangle has all four of
its
vertices on a circle. find the corcumference
of the circle​

Answer 1

Answer:

as its radius =2√5÷2(diagonal will become diameter) therefore it's circumference = 2×3.14×(2√5÷2)

Answer 2

Answer:

Circumference of circle is 28.1cm

Step-by-step explanation:

The measurement of the circle's perimeter, also known as its circumference, is called the circle's boundary. The region a circle occupies is determined by its area. If we open a circle and make a straight line out of it, then its length is the circumference.

The Circumference (or) perimeter of circle = 2πR

where,

R is the radius of the circle

π is the mathematical constant with an approximate (up to two decimal points) value of 3.14

Again,

Pi (π) is a special mathematical constant; it is the ratio of circumference to diameter of any circle.

Given: A 2 cm by 4 cm rectangle has all four of its vertices on a circle.

find: the circumference of the circle​.

As shown in figure:

Diagonal of rectangle can be find using Pythagoras Theorem:

$AC^{2} =AB^2+BC^2$

$AC^2=4^2+2^2\\AC^2=16+4\\AC^2=20\\AC=\sqrt{20} \\AC=2\sqrt{5} cm$

AC diagonal is radius of the circle.

So,

R=$2\sqrt{5} cm$

Circumference of circle= 2πR

Circumference $=2\times3.14\times2\sqrt{5}$

Circumference$=28.085cm$

#SPJ2