1. First, according to the conditions in the problem, we can find the lengths of CD, AH, AC, HO, CO, AD and AB.
2. Connecting DE and EC proves that d EC is similar to AFC, and the side length ratio of two triangles is DC:AC.
3. According to the conclusion in 2, it can be proved that FEC is similar to ADC, FC=CE, and the angle FDE is a right angle.
4. Let DE = X. According to the above conclusion, the lengths of DF, FE, FC and AF can be expressed by X, and the length of AE can be obtained.
5. Make the vertical line of AE pass through point C, the vertical foot is X, the vertical foot of AE passes through point D, and the vertical foot is Z, so that the intersection of CD and AE is Y. ..
6. Obviously, FDZ is similar to ADH and CXF is similar to CHO. According to the proportional relationship, the length of DZ and CX can be expressed by X. ..
7. Obviously DZY is similar to CXY, so the ratio relationship between DY and YC can be calculated from 6, and then the lengths of DY, CY and HY can be calculated.
8. The length of 8.AY can be found by Pythagorean theorem. Now we know the specific lengths of AY, AH and AB, and the length of AE can be represented by X.
9.AYH is similar to Abe. According to the proportional relationship, the value of x can be found, and then the length of AF can be found.