Question

A circle has a diameter

Answer 1

The circumference of circle is 20.096 units

Solution:

Given that circle has a diameter  with endpoints at (10, 8)  and (5, 4)

To get the diameter, find the distance between the end points

The distance between two points is given by formula;

$d=\sqrt{\left(x_{2}-x_{1}\right)^{2}+\left(y_{2}-y_{1}\right)^{2}}$

Here the points are (10, 8)  and (5, 4)

$(x_1, y_1) = (10, 8)\\\\(x_2, y_2) = (5, 4)$

Substituting the values we get,

$\begin{aligned}&d=\sqrt{(5-10)^{2}+(4-8)^{2}}\\\\&d=\sqrt{(-5)^{2}+(-4)^{2}}=\sqrt{25+16}=\sqrt{41}\end{aligned}$

$d = \sqrt{41} = 6.4$

Thus the diameter is 6.4 units

The  circumference of the circle is given by formula:

$c = \pi d$

Where "d" is the diameter of circle

$c = 3.14 \times 6.4 = 20.096$

Thus circumference of circle is 20.096 units