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读了本刊1984年第二期转载的《几何学中的四颗小明珠》一文,很受启发。笔者试图用三角法给出第三颗小明珠的证明。通过有趣的探索,得出证明如下, 命题如图,在△OA_1A_2中,∠O=20°,OA_1=OA_2,∠OA_2X=20°,∠OA_1y=30°,求θ角。即∠A_2XY。分析为了求得θ角的大小,可设法列出满足题设条件的关于θ角的三角方程。为此就要引入适当的参数并应用正弦定理列出一些关系式,然后消去所引参数,即可得到关于θ的三角方程。求解此三角方程即可使问题获解。解∵∠O=20°,
I was inspired by the article “Four Small Pearls in Geometry” reproduced in the second issue of the magazine in 1984. The author tried to give a proof of the third small pearl with the trigonometry. Through an intriguing exploration, it is proved that the proposition is as follows. In △OA_1A_2, ∠O=20°, OA_1=OA_2, ∠OA_2X=20°, ∠OA_1y=30°, and θ angle. That is, A_2XY. Analysis To find the size of the angle θ, try to list the trigonometric equations about the angle θ that satisfy the condition. To do this, we must introduce appropriate parameters and apply sine theorem to list some relations, and then eliminate the parameters we have quoted to obtain the trigonometric equation about θ. Solving this trigonometric equation can solve the problem. Solution O=20°,