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

`Delta = r xx s`
`:. (21 xx r)/(2) = (6 xx h)/(2) = 3h`
or `(r)/(h) = (2)/(7)`
Now APQ and ABC are similar. Thus,
`(h -r)/(h) = (PQ)/(6)`
or `1 - (r)/(h) = (PQ)/(6)`
or `1 - (2)/(7) = (PQ)/(6)`
or `(5)/(7) = (PQ)/(6) " or " PQ = (30)/(7)`