SupposethatinFig.2，thelengthofsideofsquareABCDis1，EandFaremid-pointsofCDandADrespectively，GEandCFintersectatapointP．ThenthelengthoflinesegmentCPis5555．（英汉词典：figure（缩写Fig．）图；length

Question

Suppose that in Fig.2，the length of side of square ABCD is 1，E and F are mid-points of CD and AD respectively，GE and CF intersect at a point P．Then the length of line segment CP is

(√(5))/(5)

(√(5))/(5)

．（英汉词典：figure（缩写Fig．）图；length 长度；square 正方形；mid-point中点；intersect 相交；line segment 线段）

Answer 1

∵四边形ABCD是正方形
∴△CDF≌△BCE
∴∠DFC=∠BEC
∵∠DFC+∠DCF=90°
∴∠BEC+∠DCF=90°
∴∠EPC=90°
∴△ECP∽△ECB，
∵BC=1，EC=(1)/(2)DC=(1)/(2)
∴BE=√(12+((1)/(2))2)=(√(5))/(2)
∵(BC)/(CP)=(BE)/(CE)
∴(1)/(CP)=((√(5))/(2))/((1)/(2))
∴CP=(√(5))/(5)．
故答案为(√(5))/(5)．