In fig., DE ∥ BC and CD ∥ EF. Prove that AD2= AB x AF.
In △ABC, we have
DE∥BC
⇒ ABAD = ACAE ........ (i)
In △ADC, we have
FE ∥ DC
⇒ ADAF = ACAE ........ (ii)
From (i) and (ii), we get
ABAD = ADAF
AD2 = AB × AF