182 CHAPTER 3 Foundations of Geometry 2 (b) Drag Cto such a position that ray BC lies exterior to LBAB', What happens to the locus of D in this case? Is your knowledge of Euclidean geometry sufficient for you to explain this behavior? 3.7 Quad (a) (b) MLCBA = 32.64° %3D mZCBA = 11.95° A B D. 10. Assume the usual definition for circles. Consider the concentric circles in the figure, and show that if OA and OB are radii of the smaller of the two circles, and LOAC =LOBD, then AC = BD. 11. Prove that if I is any point on the bisector BD of LABC, then I is an interior point of the angle and is equidistant from its sides, and conversely. *12. Prove that the angle bisectors of any triangle are concurrent at a point I, called the incenter, that is equidistant from the three sides of the triangle. (Hint: Use the re- sult of Problem 11; the argument is virtually the same as that for the concurrence of the perpendicular bisectors of the sides of a triangle, Problem 20, Section 3.3.) D *This result is needed for Problem 14, Section 3.8.