Find the degree measure of each central angle or inscribed angle indicated below. 10. mZZOW (84) myz = 80 Z 11. mZYWZ (87) From each given statement below, select the definition, property, postulate, or theorem that justifies each prove statement. Refer to the diagram below for problems 12 & 13. 12. Given: LM is a diameter of OO . (82) Prove: ZLNM is a right angle. A. Definition of a diameter B. An inscribed angle that intercepts a semicircle is a right angle. N C. Definition of a right angle D. In a circle, a diameter drawn perpendicular to a chord bisects the minor are that the chord intercepts. M E. The degree measure of a minor arc is the measure of its central angle. 13. Given: PO is tangent to OO at point P. (82) Prove: OP 1 PQ A. If a line through the center of a circle is perpendicular to a chord, it also bisects the chord. B. If a radius is drawn to the point of tangency of a tangent line, then the radius is perpendicular to the tangent line. C. In the same circle, all radii are congruent. D. In the same circle, if any radii are perpendicular to two chords, then the chords are congruent. E. If a radius is perpendicular to a line at the point where the line intersects a circle, then the line is a tangent line. Answer each question below. 14. A median of an equilateral triangle measures 5v3 centimeters. What is the perimeter of the (76) equilateral triangle? 15. Find the lengths of the legs of a right triangle where one acute angle measures 65 degrees and the 79) hypotenuse measures 12. Estimate each answer to two decimal places. 16. AABC ~ AXYZ with a ratio of similitude of 8:3. Also, XZ is 1 less than AB and BC is 4 more than AC. (65) If XY =9, what is YZ