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 .
Hypotenuse of a right triangle is 25 cm and out of the remaining two sides, one is longer than the other by 5 cm. Find the lengths of the other two sides.
Legs (sides other than the hypotenuse) of a right triangle are of lengths 16cm and 8 cm. Find the length of the side of the largest square that can be inscribed in the triangle.
Is it true to say that if in two triangles, an angle of one triangle is equal to an angle of another triangle and two sides of one triangle are proportional to the two sides of the other triangle, then the triangles are similar? Give reasons for your answer.
D is a point on side QR of ΔPQR such that PD⊥QR. Will it be correct to say that ΔPQD∼ΔRPD? Why?
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