AMSCO'S Geometry. New York - Rye High School

552 Geometry of the Circle18. If AB 18 and OB 15, find OC. 19. If AB 20 and OB 15, find OC.20. If mAOB 90, and AB 30"2, find 21. If mAOB 60, and AB 30, findOB and DE.OB and OC.22. In circle O, chord LM is 3 centimeters from the center and chord RS is 5 centimeters fromthe center. Which is the longer chord?Applying Skills23. Prove Theorem 13.3b, “In a circle or in congruent circles, congruent chords have congruentcentral angles.”24. Prove Theorem 13.4b, “In a circle or in congruent circles, congruent chords have congruentarcs.”25. Diameter AOB of circle O intersects chord CD at E and bisects CDX at B. Prove that AOBbisects chord CD and is perpendicular to chord CD.26. The radius of a spherical ball is 13 centimeters. A piece that has a plane surface is cut off ofthe ball at a distance of 12 centimeters from the center of the ball. What is the radius of thecircular faces of the cut pieces?27. Triangle ABC is inscribed in circle O. The distance from the center of the circle to AB isgreater than the distance from the center of the circle to BC, and the distance from the centerof the circle to BC is greater than the distance from the center of the circle to AC.Which is the largest angle of ABC? Justify your answer.13-3 INSCRIBED ANGLES AND THEIR MEASURESBIn the diagram, ABC is an angle formed by two chords that have a commonendpoint on the circle.ACDEFINITIONAn inscribed angle of a circle is an angle whose vertex is on the circle and whosesides contain chords of the circle.We can use the fact that the measure of a central angle is equal to the measureof its arc to find the relationship between ABC and the measure of its arc,ACX .