A triangle has sides 6,7, and 8. The line through its incenter parallel to the shortest side is drawn to meet the other two sides at P and Q. Then find the length of the segment PQ.

Explanation

We can draw the diagram with the given details.
Please refer to video to see the diagram.

Now, `Delta = r**s = r**(a+b+c)/2 = r**(6+7+8)/2 = 21/2r`

`:. Delta = 21/2 r->(1)`

From the diagram, we can see that,

`Delta = 1/2**h**BC = 1/2**h**6 = 3h`

`:. Delta = 3h->(2)`

From (1) and (2),

`=>21/2r = 3h => r/h = 2/7`

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