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;
[tex]d=\sqrt{\left(x_{2}-x_{1}\right)^{2}+\left(y_{2}-y_{1}\right)^{2}}[/tex]
Here the points are (10, 8) and (5, 4)
[tex](x_1, y_1) = (10, 8)\\\\(x_2, y_2) = (5, 4)[/tex]
Substituting the values we get,
[tex]\begin{aligned}&d=\sqrt{(5-10)^{2}+(4-8)^{2}}\\\\&d=\sqrt{(-5)^{2}+(-4)^{2}}=\sqrt{25+16}=\sqrt{41}\end{aligned}[/tex]
[tex]d = \sqrt{41} = 6.4[/tex]
Thus the diameter is 6.4 units
The circumference of the circle is given by formula:
[tex]c = \pi d[/tex]
Where "d" is the diameter of circle
[tex]c = 3.14 \times 6.4 = 20.096[/tex]
Thus circumference of circle is 20.096 units
