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ABCD is a rhombus. A straight line through C cuts AD produced at P and AB produced at Q. If DP = ( 1/2 )AB, then the ratio of the length of BQ and AB is
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- 2 : 1
- 1 : 2
- 1 : 1
- 3 : 1
- 2 : 1
Correct Option: A
According to question , we draw a figure of rhombus ABCD and straight line through C cuts AD produced at P and AB produced at Q , 
AB = BC = CD = DA
[ABCD is a rhombus]
| DP = | AB = | BC = | CD = | DA | ||||
| 2 | 2 | 2 | 2 |
In ∆s APQ and BCQ,
∴ ∆ APQ and ∆ BCQ are similar.
| ∴ | = | ||
| BQ | BC |
| ⇒ | + 1 = | = | |||
| BQ | BC | 2 |
| ⇒ | = | - 1 = | |||
| BQ | 2 | 2 |
| ⇒ | = | ||
| AB | 1 |
⇒ BQ : AB = 2 : 1
