Question

Test your intelligence

Answer 1

In ΔDOC and ΔBOA,

• ∠CDO = ∠ABO (Alternate interior angles as AB || CD)
• ∠DCO = ∠BAO (Alternate interior angles as AB || CD)
• ∠DOC = ∠BOA (Vertically opposite angles)

Therefore,

ΔDOC ∼ ΔBOA [ BY AAA similarity]

Implies,

OA/OC = OB/OD (Corresponding sides of similar triangles are proportional)

or,

AO/OC = BO/DO

[Hence: Proved] Q.E.D