Question:
In \( \triangle ABC \), if \( r_1 : r_2 = 7:8 \) and \( r_1 : r_3 = 3:4 \), then \( a : b : c = \)
In \( \triangle ABC \), if \( r_1 : r_2 = 7:8 \) and \( r_1 : r_3 = 3:4 \), then \( a : b : c = \)
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When the ratio of inradii is given, the ratio of sides is directly proportional to these ratios.
Updated On: May 13, 2025
- \( 24 : 21 : 28 \)
- \( 8 : 7 : 6 \)
- \( 13 : 14 : 15 \)
- \( 7 : 8 : 6 \)
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The Correct Option is C
Solution and Explanation
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:
\[
a : b : c = 13 : 14 : 15
\]
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