Using ruler and compasses only, construct a parallelogram ABCD using the following data: AB = 6 cm, AD = 3 cm and ∠DAB=45∘. If the bisector of ∠DAB a meets BC at P, prove that ∠APB is right angle.

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How many perfect cubes can you find from 1 to 100? How many from -100 to 100?