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JEE Main 2005
Exam
JEE Main
Year
2005
Subject
Mathematics
Chapter
Properties of Triangles

JEE Main 2005 · Mathematics · Properties of Triangles

ABC is a triangle. Forces P , Q , R acting along I A, I B and I C...

ABC is a triangle. Forces P⃗,Q⃗,R⃗\vec{P}, \vec{Q}, \vec{R} acting along IA,IBI A, I B and ICI C respectively are in equilibrium, where II is the incentre of △ABC\triangle A B C. Then P:Q:RP: Q: R isABC is a triangle. Forces P , Q , R acting along I A, I B and I C respectively are in equilibrium, where I is theABC is a triangle. Forces P , Q , R acting along I A, I B and I C respectively are in equilibrium, where I is the

Options

  1. Asin⁡A:sin⁡B:sin⁡C\sin A: \sin B: \sin C
  2. Bsin⁡A2:sin⁡B2:sin⁡C2\sin \frac{A}{2}: \sin \frac{B}{2}: \sin \frac{C}{2}
  3. Ccos⁡A2:cos⁡B2:cos⁡C2\cos \frac{\mathrm{A}}{2}: \cos \frac{\mathrm{B}}{2}: \cos \frac{\mathrm{C}}{2}
  4. Dcos⁡A:cos⁡B:cos⁡C\cos A: \cos B: \cos C

Correct answer

C. cos⁡A2:cos⁡B2:cos⁡C2\cos \frac{\mathrm{A}}{2}: \cos \frac{\mathrm{B}}{2}: \cos \frac{\mathrm{C}}{2}

Step-by-step solution

ABC is a triangle. Forces P , Q , R acting along I A, I B and I C respectively are in equilibrium, where I is the
Using Lami's Theorem \therefore P: Q: R=\cos A2\frac{A}{2}: \cos B2\frac{B}{2}: \cos C2. \frac{C}{2} \text{. }
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