A square is inscribed in a circle of radius 5 centimeters. What is the value of x^2 + y^2?
What is the value of x^2 + y^2?
Draw the diagonal of the square that connects the end points of x and y.
The line you just drew serves as three components we're interested in.
It's the diagonal of the square.
It's the diameter of the circle.
It's the hypotenuse of a right triangle.
Since it's the hypotenuse, its square is equal to the sum of the squares of the other two sides.
The square of the hypotenuse is 102 = 100.
Therefore x2 + y2 = 100