Question

in ∆ CAB, points D and F are on the sides AC and E is on side BC such that DE || AC and FE || DB

Prove That: (DC)² - (FC)² = FC × AF​

Answer 1

Answer:

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Step-by-step explanation:

In ΔABC,  we have  CD/DA = CE/EB      as AB || DE

in ΔCDB,  we have  CF/FD = CE/EB     as  EF || BD

hence we get   CD/DA = CF/FD

=> Reciprocals:     DA/CD = FD /CF

=> Add 1 on both sides:     AC /CD = DC/CF

=>    DC^2 = CF * AC