CDS 2017 PYQ with Answer — In a trapezium ABCD, AB is parallel to CD and the diagonals intersect…

2017 · Q86

In a trapezium ABCD, AB is parallel to CD and the diagonals intersect each other at O. What is the ratio of OA to OC equal to ?

Elementary MathematicsQuadrilaterals and Polygons

ARatio of OB to OD
BRatio of BC to CD
CRatio of AD to AB
DRatio of AC to BD

Explanation

This is a similar-triangles application. AB ∥ CD makes the alternate interior angles equal (∠OAB = ∠OCD, ∠OBA = ∠ODC), so ΔAOB ∼ ΔCOD with the correspondence A↔C, B↔D. Therefore OA/OC = OB/OD. Option (b) is the trap from pairing non-corresponding sides. Hence option (a).