Question

The exradii of a triangle \( r_1, r_2, r_3 \) are in harmonic progression, then the sides \( a, b \) and \( c \) are in

• A. \( (-0, 1) \)
• B. \( (2, 3) \)
• C. \( (-0, 3) \)
• D. \( (-0, 1) + (2, 3) \)

Hint:

In problems involving harmonic progressions, use the condition that the reciprocals of the terms must be in arithmetic progression.

Answer 1

The Correct Option is B

For the exradii \( r_1, r_2, r_3 \) to be in harmonic progression, it implies that the sides \( a, b, c \) of the triangle will be in the harmonic progression that results from this condition. The solution gives the value \( (2, 3) \) for the sides.