In a parallelogram PQRS, PX and QY are the perpendiculars drawn from P and Q respectively so SR and SR produced. Prove that PX= QY.

PQRS is a parallelogram.PX and QY are respectively,the perpendiculars from P and Q to SR and RS produced.Frove that PX=QY.

In a parallelogram PQRS, PQ = 12 cm and PS = 9 cm. The bisector of angle P meet SR in M. PM and QR both when produced meet at T. Find the length of RT.

In the adjoining figure, PQRS is a parallelogram. A and B are the mid-points of PQ of SR respectively. If PS= BR, then prove that quadrilateral ADBC is a reactangle.

In the adjoining figure, QX and RX are the bisectors of the angles Q and R respectively of the angles Q and R respectively of the triangle PQR. If XS bot PQ . Prove that : (i) DeltaXTQ cong DeltaXSQ (ii) PX bisects angle P.

Perpendiculars are drawn,respectively,from the points P and Q to the chords of contact of the points Q and P with respect to a circle. Prove that the ratio of the length of perpendiculars is equal to the ratio of the distances of the points P and Q from the center of the circles.

PQRS is a parallelogram.PS is produced to M, so that SM=SR and MR produced meets PQ produced at N. Prove that QN=QR

PQRS is a parallelogram.PS is produced to M, so that SM=SR and MR produced meets PQ produced at N. Prove that QN=QR

In the adjoining figure,PQR,is a right triangle,right angled at C .X and Y are the points on PQ and QR such that PX:XQ=1:2 and QY:YR=2:1. Prove that 9(PY^(2)+XR^(2))=13PR^(2)