Given: ∆ ABC and ∆ DBC have the same base BC.
AD and BC intersect at O.
First, we construct the altitudes, AE and DF, of ∆ ABC and ∆ DBC, respectively.
Consider, ∆ AOE and ∆ DOF,
∠DFO = ∠AEO [Right angles]
∠DOF = ∠AOE [Vertically Opposite angles]
So, by AA criterion,
∆AOE ∼ ∆DOF
⇒ Ratio of all the corresponding sides of ∆ AOE and ∆ DOF are equal.
Now, we know that
Dividing (ii) by (iii),
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