题干

某市为方便相距2km的A、B两处居民区的交往,修筑一条笔直的公路(如图:AB),经测量,在A处的北偏东60°方向,B处北偏西45°方向的C处有一半径为0.7km的圆形公园,问计划修筑的公路会不会穿过公园?请说明理由.

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答案(点此获取答案解析)

解:如图所示,过点C作CD⊥AB,垂足为点D,

由题意可得:∠CAB=30°,∠CBA=45°,

在Rt△CDB中,∠BCD=45°,

∴∠CBA=∠BCD,∴BD=CD.

在Rt△ACD中,∠CAB=30°,

∴AC=2CD.

设CD=DB=x,

∴AC=2x.

由勾股定理得AD=A<

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