Acute triangle is given. The angle at point C is 45 . Points A1 and B1 are the feet of the altitudes from points A and B, respectively . Let point H be an orthocenter of a triangle. On segments AA1 and BC and are points D and E, respectively, so that $\displaystyle A1D=A1E=A1B1$ . Prove that:

1. $\displaystyle CH=DE$

2.$\displaystyle A1B1^2=(A1B^2+A1C^2)/2$