Question

In \( \triangle ABC \), if \( r_1 : r_2 = 7:8 \) and \( r_1 : r_3 = 3:4 \), then \( a : b : c = \)

• A. \( 24 : 21 : 28 \)
• B. \( 8 : 7 : 6 \)
• C. \( 13 : 14 : 15 \)
• D. \( 7 : 8 : 6 \)

Hint:

When the ratio of inradii is given, the ratio of sides is directly proportional to these ratios.

Answer 1

The Correct Option is C

We know the relationship between the sides and the inradii: \[ r_1 : r_2 = 7 : 8 \quad \text{and} \quad r_1 : r_3 = 3 : 4 \] Thus, the ratio of sides \( a : b : c \) is proportional to the inradii: \[ a : b : c = 13 : 14 : 15 \]