In the circle below, PQ is parallel to diameter OR. OR has length 18. What is th

游客2024-01-12 16

问题 In the circle below, PQ is parallel to diameter OR. OR has length 18. What is the length of minor arc PQ?

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答案 2π

解析求与弧相关的数量，如弧长、扇形面积等，需先求出弧所对的圆心角的大小。求角度时，可利用目前已知的角度，通过平行、垂直等条件推出目标所求的角度。圆周角∠R=35°，所以所对的弧OP的角度是35°×2=70°。又因为PQ平行于OR，所以∠P=∠R=35°(内错角)，圆周角∠P所对的弧QR的度数是70°。因为OR是直径，所以，弧OR(上半部分)的角度是180°。所以，弧PQ的角度是弧OR-弧OP-弧QR=180°-70°-70°=40°。同时已知OR直径长为18，则半径长为9。代入弧长公式，得弧PQ的弧长l=40×π×9/180=2π。

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