ABCD is a trapezium in which AB || DC and P and Q are the points on AD and BC, respectively such that PQ || DC. If PD = 18 cm, BQ = 35 cm and QC = 15 cm, then AD = _________.
If ∆ABC ∼ ∆DEF, AB = 4 cm, DE = 6, EF = 9 cm and FD = 12 cm, then find the perimeter of ∆ABC.
In figure, if AB || DC and AC, PQ intersect each other at the point O. Prove that OA.CQ = OC.AP.
Diagonals of a trapezium PQRS intersect each other at the point O, PQ || RS and PQ = 3RS. Find the ratio of the areas of triangles POQ and ROS.
In a ΔPQR, PR2−PQ2=QR2 and M is a point on side PR such that QM⊥PR. Prove that QM2 = PM × MR .
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