In trapezium ABCD, AB \(\parallel\) DC and the diagonals AC and BD intersect at point O. Given: OA = 2 × OC and AB = 10 cm. Find: The length of DC.

Q.In trapezium ABCD, AB \(\parallel\) DC and the diagonals AC and BD intersect at point O. Given: OA = 2 × OC and AB = 10 cm. Find: The length of DC. (a) 4 cm (b) 5 cm (c) 6 cm (d) 8 cm

Answer: B

In triangles OAB and OCD: \(\angle\)OAB = \(\angle\)OCD \(\angle\)OBA = \(\angle\)ODC ∴ Triangles OAB and OCD are similar. ∴ \(\cfrac{OA}{OC} = \cfrac{AB}{DC}\) i.e., \(\cfrac{2OC}{OC} = \cfrac{10}{DC}\) ⇒ \(DC = 5\) ∴ DC = 5 cm.