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In ∆ABC, the line parallel to BC intersects AB and AC at P and Q respectively. If AB : AP = 5 : 3, then AQ : QC is :
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- 3 : 2
- 2 : 3
- 3 : 5
- 1 : 2
- 3 : 2
Correct Option: A
On the basis of given in question , we draw a figure of an equilateral triangle ABC ,
From figure , PQ || BC
Given , AB : AP = 5 : 3
∴ ∠APQ = ∠ABC
∠AQP = ∠ACB
∴ By AA - similarity theorem,
∆ APQ ~ ∆ ABC
| ∴ | = | = | |||
| AP | AQ | 3 |
| ⇒ | - 1 = | - 1 | ||
| AQ | 3 |
| ⇒ | = | ||
| AQ | 3 |
| ⇒ | = | ||
| AQ | 3 |
| ∴ | = | ||
| QC | 2 |
