Equilateral triangle: circumradius, inradius and centroid distances from the side

This type of question, asked 3 times: 24 Jul 2023 S1, 24 Jul 2023 S3, 17 Sep 2025 S2. All 3 questions below, oldest first.

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Question 1
24 Jul 2023 S1
67 $The length of each side of a triangle is 12 cm. What is the length of the circumradius of the triangle?$
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Question 2
24 Jul 2023 S3
67 $The centroid of an equilateral triangle PQR is L. If PQ = 6 cm, the length of PL is:$
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Question 3
17 Sep 2025 S2
67 $In an equilateral triangle with side length 'a', what is the ratio of the circumradius to the inradius?$
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Question 1