A square is inscribed in a circle such that each corner touches the circle. A. Find a function that gives the area of the square as a function of the radius of the circle. Simplify the function as much as possible, and describe any symmetry in the function. Make certain to show all the steps you use to come up with the function, as well as describe your reasoning B. State the domain and range of the function you came up with in part (A), keeping in mind all practical considerations.
Accepted Solution
A:
Answer:A(r) = √2 * rA(r) Domain is R { r ; r > 0}Step-by-step explanation:Diagonals of a square intercept each other in a 90° angle. The four triangles resulting from diagonal interception are equal and are isosceles triangles, with hipotenuse a side of the squareTherefore we apply Pythagoras theorem Let x be side of square, and r radius of the circle, ( diagonals touch the circle) thenx² = r² + r²x² = 2r²x = √2 * rNow Aea of square is :A = L² where L is square sideA(r) = √2 * rDomain of A(r) = R { r, r > 0}