In a triangle PQR, S and T are points on QR and PR respectively, such that QS=3SR and PT=4TR. Let M be the point of intersection of PS and QT. Determine the ratio QM:MT

In the figure, angleQPR = anglePQR and M and N are respectively on sides QR and PR such that QM = PN. Prove that OP=OQ, where O is the point of intersection of PM and QN.

In the fig. angleQPR=anglePQR and L and M are respectively on sides QR and PR of PQR such that QL=PM prove that OP=OQ, where O is the point of intersection of PL and QM

In the adjoining figure, S and T are points on the sides PQ and PR respectively of DeltaPQR such that PT=2cm, TR=4 cm and ST is parallel to QR. Find the ratio of the ares of Delta PST and Delta PQR .

In a square PQRS, X and Y are mid points of sides PS and QR respectively. XY and QS intersect a t O. Find the area of Delta XOS, if PQ = 8 cm.

In the adjacent figures, S and T are points on the sides PQ and PR respectively of triangle PQR such that PT = 2cm, TR = 4cm and ST||QR . Find the ratio of the areas of triangle PST and triangle PQR .

In a triangle PQR, anglePQR = 90^@ S is any point onQR. Prove that PS^2+QR^2 = PR^2+QS^2 .