alleryIn a quadrilateral ABCD where AB is parallel to CD and the diagonals AC and BD intersect at O, the ratio AO : OC equals
ABO : OD
BOD : BO
CAB squared : CD squared
DCD : AB
Answer & Solution
Correct answer: A. BO : OD
1. Triangles AOB and COD are similar by AA (AB parallel to CD gives equal alternate angles).
2. Corresponding sides are in proportion: AO/OC = BO/OD.
3. Hence AO : OC = BO : OD.
_Source: syllabus Mathematics, Ch 6 "Triangles", §6.4_
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