AMSCO'S Geometry. New York - Rye High School

578 Geometry of the CirclePSolution Since ST TR SR 9, let ST x and TR 9 x.R(PT)(TQ) 5 (RT)(TS)(2)(10) 5 x(9 2 x)2T10O20 5 9x 2 x 2Qx 2 2 9x 1 20 5 09S(x 2 5)(x 2 4) 5 0x 2 5 5 0 x 2 4 5 0x 5 5 x 5 49 2 x 5 4 9 2 x 5 5Answer ST 5 and TR 4, or ST 4 and TR 5EXAMPLE 3Find the length of a chord that is 20 centimeters from the center of a circle if thelength of the radius of the circle is 25 centimeters.Solution Draw diameter COD perpendicular to chord AB at E.Then OE is the distance from the center of the circle tothe chord.OE 20 DE 5 OD 1 OE CE 5 OC 2 OE5 25 1 205 25 2 205 455 5A diameter perpendicular to a chord bisects the chord. Therefore, AE EB.Let AE EB x.(AE)(EB) 5 (DE)(CE)(x)(x) 5 (45)(5)x 2 5 225x 5 15 (Use the positive square root.)Therefore,AB 5 AE 1 EB5 x 1 x5 30 cm AnswerA5 cm20 cmO25 cmCED25 cmB