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The medians CD and BE of a triangle ABC intersect each other at O. The ratio ∆ ODE : ∆ ABC is equal to
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- 12 : 1
- 4 : 3
- 3 : 4
- 1 : 12
- 12 : 1
Correct Option: D
On the basis of question we draw a figure of triangle ABC in which the medians CD and BE intersect each other at O ,
In ∆ ADE and ∆ ABC,
∠ADE = ∠ABC
∠AED = ∠ACB
∴ ∆ AED ~ ∆ ABC
| ∴ | = | ||
| AB | BC |
| ⇒ | = 1 | |
| DB |
| ⇒ | + 1 = 2 | |
| AD |
| ⇒ | = 2 | |
| AD |
| ⇒ | = 2 ⇒ | = | |||
| AD | AB | 2 |
| ⇒ | = | ||
| BC | 2 |
| ∴ | = |  |  | ² | = | |||
| ∆ BOC | 2 | 4 |
| ∴ | = | = 1 : 12 | ||
| ∆ ABC | 12 |
[∵ 3 ∆ BOC = ∆ ABC]
