Question

In an equilateral triangle, the inradius, circumradius, and one of the exradii are in the ratio:

• A. 2 : 3 : 5
• B. 1 : 2 : 3
• C. 1 : 3 : 7
• D. 3 : 7 : 9

Hint:

In an equilateral triangle, the inradius, circumradius, and exradius follow a known ratio derived from the side length.

Answer 1

The Correct Option is B

Step 1: Use properties of the equilateral triangle.
The relationships between the inradius, circumradius, and exradius are well-known for an equilateral triangle and can be derived based on the side length.
Step 2: Conclusion.
Thus, the ratio is \( 1 : 2 : 3 \).
Final Answer: \[ \boxed{1 : 2 : 3} \]