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In the circle below, PQ is parallel to diameter OR. OR has length 18. What is th
In the circle below, PQ is parallel to diameter OR. OR has length 18. What is th
游客
2024-01-12
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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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