In the parallelogram ABCD, the line drawn through a point P on AB, parallel to BC, meets AC at Q. The line through Q, parallel to AB meets AD at R.
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In ΔABC, RQ the parallel line of BC, divides AB and BC in the same ratio When we consider the relation A R R D = A Q Q C , A P P B = A Q A C = A R R D ARRD=AQQC,APPB=AQAC=ARRD A R R D = A Q Q C ARRD=AQQC A P P B = A Q A C = A R R D APPB=AQAC=ARRD ∴ A P P B = A R R
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