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In the DeltaABC, altitudes AD and CE int...

In the `DeltaABC`, altitudes AD and CE intersect each other at point P. Prove that

i] `DeltaAPE~DeltaCPD`
ii] `APxxPD=CPxxPE`
iii] `DeltaADB~DeltaCEB`
iv] `ABxxCE=BCxxAD`

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