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Through each vertex of a triangle, a line parallel to the opposite side is drawn. The ratio of the perimeter of the new triangle, thus formed, with that of the original triangle is
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- 3 : 2
- 4 : 1
- 2 : 1
- 2 : 3
- 3 : 2
Correct Option: C
AQ || CB ,and AC || QB
∴ AQBC is a parallelogram
⇒ BC = AQ Again,
AR || BC and AB || RC
∴ ARCB ,is a parallelogram.
⇒ BC = AR ⇒ AQ = AR
| ⇒ AQ = AR = | QR | |
| 2 |
| ⇒ BC = | QR | |
| 2 |
| Similarly, AB = | RP and AC = | PQ | ||
| 2 | 2 |
∴ Required ratio = (PQ + QR + RP) : (AB + BC + CA) = 2 : 1
