ABCD is a trapezium with AD ∥ BC and AD = 4 cm. If the diagonals AC and BD intersect each other at O such that AO/OC = DO/OB = 1/2, then BC =
(a) 6 cm (b) 7 cm (c) 8 cm (d) 9 cm

CBSE Class 10 Sample Paper for 2023 Boards - Maths Standard
CBSE Class 10 Sample Paper for 2023 Boards - Maths Standard
Last updated at Dec. 13, 2024 by Teachoo
ABCD is a trapezium with AD ∥ BC and AD = 4 cm. If the diagonals AC and BD intersect each other at O such that AO/OC = DO/OB = 1/2, then BC = (a) 6 cm (b) 7 cm (c) 8 cm (d) 9 cm In Δ AOD and Δ BOC ∠ AOD = ∠ BOC 𝐴𝑂/𝑂𝐶=𝐷𝑂/𝑂𝐵 ∴ Δ AOD ~ Δ BOC Since both triangles are similar Their sides will be in proportion 𝑨𝑶/𝑶𝑪=𝑫𝑶/𝑶𝑩=𝑨𝑫/𝑩𝑪 1/2=𝐴𝐷/𝐵𝐶 Putting AD = 4 cm 1/2=4/𝐵𝐶 BC = 2 × 4 BC = 8 cm So, the correct answer is (c)