Question

ABCD is a parallelogram. AP bisects ZA and CQ bisects ZC. P lies on CD and Q
lies on AB. Show that
APICO
(6) AOCP is a parallelogram.​

Answer 1

Answer:

ANSWER

Since the circum-centres of the △ABC and △ADC i.e.. Q and R are the points of concurrence of the perpendicular bisectors of their sides. If O is the mid-point of Diagonal AC, then

∴ Diagonals of quadrilateral AQCR bisect each other respectively at right-angle and MQ and NR are the perpendicular bisectors of BC and AD. Again, the circum-centre of a triangle is equidistant from its vertices.

∴AQ=CQ=BQ

and AR=CR=DR

Hence, the quadrilateral AQCR is always a rhombus.

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