As background for Exercises 47 and 48, refer to the figure

Chapter 9, Problem 47

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As background for Exercises 47 and 48, refer to the figure below. The smaller circle in the figure is the inscribed circle for ^ABC. Each side of ^ABC is tangent to the inscribed circle. The larger circle is the circumscribed circle for ^ABC. The circumscribed circle is the circle passing through the three vertices of the triangle. In Exercises 47 and 48 you will derive expressions for the radii of the circumscribed circle and the inscribed circle for ^ABC. In these exercises, assume as given the following two results from geometry: i. The three angle bisectors of the angles of a triangle meet in a point. This point (labeled I in the figure) is the center of the inscribed circle. ii. The perpendicular bisectors of the sides of a triangle meet in a point. This point (labeled O in the figure) is the center of the circumscribed circle.