In triangle `A B C ,a : b : c=4:5: 6.` The ratio of the radius of the circumcircle to that of the incircle is____.

Explanation

To find the ratio of the radius of the circumcircle (R) to that of the incircle (r) in triangle ABC, where the sides are in the ratio \( a : b : c = 4 : 5 : 6 \), we can follow these steps:

### Step 1: Assign the sides of the triangle
Let the sides of the triangle be:
- \( a = 4k \)
- \( b = 5k \)
- \( c = 6k \)

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