Science:Math Exam Resources/Courses/MATH100/December 2019/Question 08/Hint 2

Use the angle $t$ between two diagonals of a rectangle to parameterize the rectangles inscribed in the circle, as in the first diagram below. Write the perimeter of the rectangle as a function of $R$ and $t$. This is a function of one variable (since $R$ is fixed).

Rectangle inscribed in a circle parameterized by angle.

Alternatively, use the length of the base to parameterize the rectangle as in the second diagram. Write the perimeter of the rectangle as a function of $R$ and $b$.

Rectangle inscribed in a circle parameterized by base