Question

A circle has a diameter

with endpoints at (10, 8)
and (5, 4). What is the
circumference of this
circle?​

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)}=√(25+16)=√(41)\end{aligned}`

`d = √(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 * 6.4 = 20.096`

Thus circumference of circle is 20.096 units