R is the mid-point of BC.( Enter 1 if true or 0
otherwise)
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Solution
Given: ABCD is a parallelogram. P is the mid point of CD. Q is the point on AC such that CQ=14AC PQ produced meets BC in R. Join BD, let BD intersect AC in O. O is the mid point of AC (Diagonals of parallelogram bisect each other) hence, OC=12AC OQ=OC−CQ OQ=12AC−14AC OQ=14AC OQ=CQ Therefore, Q is the mid point of OC. In △OCD, P is the mid point of CD and Q is the mid point of OC. BY mid point theorem, PQ∥OD or PR∥OD Now, In △BCD, P is the mid point of CD and PR∥BD, By converse of mid point theorem, R is the mid point of BC