Area/Ratio Lemma useful results

Triangle ABC.
D lies on BC, E on AC, F on AB.
AD,BE,CF are concurrent on P.

[ABC] denotes area of the triangle ABC.

Then:
DB/DC = [PDB]/[PDC] = [ADB]/[ADC] = [PAB]/[PAC]
And similarly for other sides.

Also:
PD/AD = [PBC]/[ABC]

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