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In ∆ ABC, a line parallel to BC intersects AB and AC at D and E. If AE = 3 AD, find the ratio BD : EC.
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- 1 : 3
- 1 : 2
- 2 : 3
- 3 : 2
- 1 : 3
Correct Option: A
According to question , we draw a figure of a triangle ABC and a line parallel to BC intersects AB and AC at D and E
In ∆ ADE and ∆ ABC,
∠D = ∠B; ∠E = ∠C
∠A = ∠A
∴ Both triangles are similar.
As we know that ,
| ∴ | = | ||
| AB | AC |
| ⇒ | = | ||
| AD | AE |
| ⇒ | - 1 = | - 1 | ||
| AD | AE |
| ⇒ | = | ||
| AD | AE |
| ⇒ | = | = | |||
| EC | AE | 3 |
