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CBSE Class 10 Answered

ABCD is a trapezium with AD ∥ BC and AD = 4cm. If the diagonals AC and BD intersect each other at O such that AO/OC = DO/OB =1/2, then BC =
Asked by supriyasupriya39.10 | 20 Jan, 2023, 08:40: PM
answered-by-expert Expert Answer
In Triangles AOD and BOC , begin mathsize 14px style angle end styleAOD = begin mathsize 14px style angle end styleBOC ( vertically opposite angles when two lines intersect )
begin mathsize 14px style fraction numerator A O over denominator O C end fraction equals fraction numerator D O over denominator O B end fraction equals 1 half end style
 
hence Δ AOD is similar to Δ BOC .
 
Hence , we have begin mathsize 14px style fraction numerator A D over denominator B C end fraction equals 1 half end style
 
BC = 2 × AD = 2 × 4 cm = 8 cm
Answered by Thiyagarajan K | 20 Jan, 2023, 10:07: PM
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