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Question
ABC is a triangle. PQ is a line segment intersecting AB in P and AC in Q such that PQ || BC and divides triangle ABC into two parts equal in area. Find the value of ratio BP : AB.
Solution
From the given information, we have:
`ar (∆APQ) = 1/2 ar(∆ABC)`
`=> (ar(ΔAPQ))/(ar(ΔABC)) = 1/2`
`=> (AP^2)/(AB^2) = 1/2`
`=> (AP)/(AB) = 1/sqrt(2)`
`=> (AB - BP)/(AB) = 1/sqrt(2)`
`=> 1 - (BP)/(AB) = 1/sqrt(2)`
`=> (BP)/(AB) = 1 - 1/sqrt(2)`
`=> (BP)/(AB) = (sqrt(2) - 1)/sqrt(2) = (2 - sqrt(2))/2`
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