Question

In the adjoining figure, if ΔAOB ~ ΔCOD, then which of the following is true?

Options

• AO.OB = OC.OD

• AO.CD = OC.AB

• AO.AB = OC.CD

• AO.OC = OB.OD

Answer 1

AO.CD = OC.AB

Explanation:

From ΔAOB ~ ΔCOD we get ∠A = ∠C and ∠B = ∠D.

In triangles AOD and COB, ∠AOD = ∠COB (vertically opposite) and ∠A = ∠C, so ΔAOD ~ ΔCOB.

Hence, corresponding sides give `(AO)/(CO) = (OD)/(OB)`; cross-multiplying gives AO.OB = OC.OD.