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, 20:40: PM
![](https://images.topperlearning.com/topper/tinymce/imagemanager/files/dfa3348e96d3df1aa2a7c9e5334cd80d63cac1d1e03be1.44734134g2.png)
In Triangles AOD and BOC ,
AOD =
BOC ( vertically opposite angles when two lines intersect )
![begin mathsize 14px style angle end style](https://images.topperlearning.com/topper/tinymce/cache/f1d45fc0daa19a85e39a8446cd27e48f.png)
![begin mathsize 14px style angle end style](https://images.topperlearning.com/topper/tinymce/cache/f1d45fc0daa19a85e39a8446cd27e48f.png)
![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](https://images.topperlearning.com/topper/tinymce/cache/44714f7976aa67877befb540c1791a54.png)
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](https://images.topperlearning.com/topper/tinymce/cache/9f21e203dbb627b8c560df523fe5ca5e.png)
![begin mathsize 14px style fraction numerator A D over denominator B C end fraction equals 1 half end style](https://images.topperlearning.com/topper/tinymce/cache/9f21e203dbb627b8c560df523fe5ca5e.png)
BC = 2 × AD = 2 × 4 cm = 8 cm
Answered by Thiyagarajan K | 20 Jan, 2023, 22:07: PM
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