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)
Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.
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