Question

If \( a, b, c \) are in HP, then \( \frac{a}{b+c} = \frac{b}{c+a} = \frac{c}{a+b} \) will be in:

• A. AP
• B. GP
• C. HP
• D. None of these

Hint:

If three numbers are in harmonic progression, their reciprocals are in arithmetic progression.

Answer 1

The Correct Option is C

Step 1: HP means Harmonic Progression.
If \( a, b, c \) are in HP, then their reciprocals are in AP. Using the properties of harmonic progression, the equation simplifies to a harmonic progression.
Step 2: Conclusion.
Thus, \( \frac{a}{b+c}, \frac{b}{c+a}, \frac{c}{a+b} \) will form a harmonic progression.
Final Answer: \[ \boxed{C} \]