Question

如图,AB⊥BC,CD⊥BC,B,C是垂足,AC,BD交于P.过P作PQ⊥BC于Q.求证:1/AB+1/CD=1/PQ

Answer 1

∵AB⊥BC,CD⊥BC,PQ⊥BC,∴AB∥PQ∥CD,

有PQ/AB=QC/BC,PQ/CD=BQ/BC,

两式相加得PQ/AB+PQ/CD=QC/BC+BQ/BC=(QC+BQ)/BC=BC/BC=1,

∴1/AB+1/CD=1/PQ.