5. [10 points) Consider the Poincar disk model for hyperbolic geometry. (a) Draw, if possible, a triangle in the Poincar disk such that all the three vertices in the triangle are ideal points. (b) Let m be a (hyperbolic) line. Define the functions:m R by f(x) - In (ADX) where A and X are two points on the line m and P and Q are the ideal points corresponding to line m. Show that f is an injective function satisfying IF(X)-f(Y) = d(X,Y) where d(X,Y) is the hyperbolic distance. 5. [10 points) Consider the Poincar disk model for hyperbolic geometry. (a) Draw, if possible, a triangle in the Poincar disk such that all the three vertices in the triangle are ideal points. (b) Let m be a (hyperbolic) line. Define the functions:m R by f(x) - In (ADX) where A and X are two points on the line m and P and Q are the ideal points corresponding to line m. Show that f is an injective function satisfying IF(X)-f(Y) = d(X,Y) where d(X,Y) is the hyperbolic distance