91Ó°ÊÓ

Let \(\triangle A B C\) be an equilateral triangle and let \(P\) be a point inside. Prove that the sum of the distances from \(P\) to the three sides of \(\triangle A B C\) is equal to the altitude \(\overline{A D}\).

Prove that if a quadrilateral \(A B C D\) is circumscribed about a circle, then the area of \(A B C D\) is one-half times the radius of the circle times the perimeter.