As?in?right?figure,in?a?quadrilateral?ABCD,we?have?its?diagonal?AC?bisects∠DAB,and?

发布时间:2020-08-12 06:48:55

As?in?right?figure,in?a?quadrilateral?ABCD,we?have?its?diagonal?AC?bisects∠DAB,and?AB=21,AD=9,BC=DC=10,then?the?distance?from?point?C?to?line?AB?is________,and?the?length?of?AC?is________.???(英汉词典:quadrilateral?四边形;bisect?平分)

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8    17
解析分析:作辅助线构建直角三角形,求证△CED≌△CFB,即可得DE=FB,即可求得BF,根据BF求CF,根据CF、AF求AC.

解答:解:过C作CE⊥AD,CF⊥AB,
∴△CED≌△CFB,
∴DE=FB,
∴9+DE=21-BF,
∴BF=6,
根据勾股定理,可知CF=CE=8,即点C到AB的距离为8.
∴AC===17.
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