To find the circumference of the circle, we first need to find its diameter.
To do so, we will start by drawing a diagonal of the inscribed polygon. Since this diagonal passes through the center of the circle, it is a diameter. As a result, we will obtain two right triangles.
Let's now focus on only one of the right triangles. We know the length of the legs and we are missing the length of the hypotenuse c, which is the diameter of the circle.
To find the length of the hypotenuse, we will substitute 8 for a and 6 for b into the Pythagorean Theorem.
Note that since c is the length of the hypotenuse of a right triangle — and the diameter of the circle — we know that it is a positive number. This is why we keep the principal root when solving the equation.
Now that we know that the diameter of the circle is 10 inches, we can calculate its circumference.
