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Prove that
27a3 + b3 + c3 - 9abc = (3a + b + c)(9a2 - bc - 3ac)




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Theorem 6.8 : In a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

11. An aeroplane leaves an airport and flies due north at a speed of 1000 km per hour. At the same time, another aeroplane leaves the same airport and flies due west at a speed of 1200 km per hour. How far apart will be the two planes after 1.5 hours?



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2. In each of the following find the value of ‘k’, for which the points are collinear.
(i) (7, –2), (5, 1), (3, k)
(ii) (8, 1), (k, – 4), (2, –5)




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32. In figure ∠Q ∠R, PA is bisector of QPR and PM ⊥ QR, Prove that APM = half of ∠Q - ∠R

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Q. 12. Evaluate each of the following by using suitable identity.
(ii) (-15)cube + (28)cube + (-13)cube

13. D and E are points on the sides CA and CB respectively of a triangle ABC right angled at C. Prove that AE2 + BD2 = AB2 + DE2.



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