Maybe that's too much work

Geometry Level 5

A triangle ABC has sides 6 ,7 , 8 units . The line through its incentre parallel to the shortest side is drawn to meet the two other sides at P and Q.

Find the length of the line segment PQ ; it is of the form \( \frac{a}{z} \) .

  • Evaluate \( a^{z} \) and express it in base \( z \). Let's name it as k .

    • Now find it's \(a^{th}\) root taking k in base 10 .
  • Report the least integer greater than it .

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