Math 083 Sample Exam 3 ____ 1. Given: Prove: ____ ABC right at A and DA ADC ~ DBA A BC . C D B C 2. Given: Prove: at C ABC right 2 2 b 2 a + b = c a A c B 3. The chords AB and CD intersect at point E, and DQ and FG are tangent to the circle. AD = 5 and m ADQ a. m ADC b. m AFC c. m AEC d. m BC e. FG 40 0 . 92 0 , DB 580 , FD = 4, If the arc AC Find Q G 4. Park rangers catch, tag, and then release 50 deer back into a wildlife refuge. Two months later they selected a sample of 108 deer, and they found out that 25 were tagged. Approximately how many deer are in the refuge? 5. Construct a tangent line to a circle from a point P on the circle. P O 6. CD bisects Find AD ACB so that AC = 8, CB = 15, and DB = 12 D B A C 7. AB is a chord of the circle Q with AB = 16. Radius QC is perpendicular to AB at D. If QC = 10, find QD. ___ 8. Given: ___ BA , BC are tangent to circle O at A and C D is midpoint of AC Find: 1 2 A O D C 1 2 B D ____ 9. Given: Prove: C ____ DC || AB I AI DI CI BI B A 10. Given: Prove: AP is the tangent line AP 2 PB PC A P B C 11) Complete each statement a) An angle inscribed in a semicircle is ______ angle. b) Two tangent segments to circle from an external point are __________. c) The length of the altitude to the hypotenuse of a right triangle is the geometric mean of the lengths of the_____________ of the ___________. d) In a circle, congruent chords have congruent __________. e) If two ________ angles of a circle intercept the same arc, then they are congruent. f) The tangent line is ________to the radius at the tangent point. g) If a ray bisects one angle of a triangle, the it divides the opposite side into ______ whose lengths are proportional to the lengths of _____ _____ that formed bisected angle.