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Question

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

A
125
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B
154
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C
307
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D
339
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Solution

The correct option is C 307

Area of ABC(Δ)=6h2=3h (where h is the altitude from A)
Also, Δ=21r2 (using Δ=rs)
21r2=3hrh=27

Now, triangle APQ and triangle ABC are similar.
hrh=PQBC1rh=PQ6127=PQ6PQ=307

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