三角形与内接圆已知三角形的内接圆与AC,AB,BC,切于D,E,F且AB=5cm BC=9cm AC=6cm 求AE,BF和CD的_数学解答

三角形与内接圆
已知三角形的内接圆与AC,AB,BC,切于D,E,F且AB=5cm BC=9cm AC=6cm 求AE,BF和CD的长

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解答

连接OA,OB,OC,OD,OE,OF
OE = OF 圆O为内切圆
==>BE = BF
同理
==>AE = AD,CD = CF
令 BF = x
==>AE = 5-x,CF = 9-x;
==>CD = 1+x;
由 CD = CF
==>1+x = 9-x
==>x = 4
==>AE = 1,BF = 4,CD = 5