Math 444 10/21/2005

Semi-quiz

Question 1. Let A' be a point on ray OA and B' be a point on ray OB. Suppose OA = a and OB = b. Also suppose that OA' = 7/a and OB' = 7/b. If AB = 10, what is the distance A'B'? (The answer should involve a, b and numbers.)

Give brief but clear reasons for your answers and calculations.

Question 2. Construct a circle tangent to the 3 sides of triangle ABC. Leave your construction marks showing. Also put in a few labels indicating the nature of key objects (for example, "m is perpendicular bisector of EF" or "circle c has center Z and passes through Y") but don't write down every step. Just be clear.