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ISI B-Stat 2011, P5: Prove that PQCD is a parallelogram

Source:

April 1, 2013

geometryparallelogramtrapezoidratio

Problem Statement

ABCD

is a trapezium such that

AB\parallel DC

and

\frac{AB}{DC}=\alpha >1

. Suppose

P

and

Q

are points on

AC

and

BD

respectively, such that

\frac{AP}{AC}=\frac{BQ}{BD}=\frac{\alpha -1}{\alpha+1}

Prove that

PQCD

is a parallelogram.