Suppose that in Fig.2，the length of

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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

∵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
2DC=
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．

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