几何证明题3

zhiwen

乌贼

如图：
直接算出来就行了，令$ DE=b,AD=b $\[ AG^2=AF^2=AD^2+DF^2+2AD\cdot DF\cdot \cos \angle ADF=a^2+b^2+ab \]\[ DG^2=DB^2=BH^2+DH^2=AB^2-AH^2+DH^2=a^2-(\dfrac{a-b}{2})^2+(\dfrac{a+b}{2})^2=a^2+ab \]则有\[ AG^2=a^2+b^2+ab=DG^2+AD^2 \]即有\[ DG\perp AE \]

zhiwen