In tetrahedral a-bcd, ab ⊥ CD, AC ⊥ BD, prove ad ⊥ BC It shouldn't be very difficult, but I just can't. help

Make the vertical line of CD through point B, and the vertical foot is m
Then the plane ABM is perpendicular to the line CD
Make the vertical line of BD through point C, and the vertical foot is n
Then the plane ACN is perpendicular to the line BD
Let the intersection of BM and cn be o, connect do, extend to BC, and intersect BC at P
Then DP ⊥ BC
The intersection of plane ABM and plane ACN is Ao
∴AO⊥BD,AO⊥CD
Ψ Ao ⊥ plane BCD
∴AO⊥BC
∵DP⊥BC
Ψ BC ⊥ plane ADP
∵ ad ∈ plane ADP
∴AD⊥BC

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