381.ABCD is a parallelogram, P is a point on side BC and DP when produced meets AB produced in L. Prove that: (i) (ii)
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382.If A is the area of a right-angle triangle and b is one of the sides containing the right angle, prove that the length of the altitude on the hypotenuse is
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Short Answer Type
383.
In the Fig, AB || DE and BD || EF. Prove that DC2 = CF × AC.
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384.The perpendicular AD on the base BC of ∆ABC meets BC at D, such that BD = 3 CD. Prove that 2(AB2 - AC2) = BC2.
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385.
In the given Fig, AD ⊥ BC if D divides BC in the ratio 1 : 3 prove that: 2 AC2 = 2AB2 + BC2.
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386.In a triangle ABC, ∠C = 90° and AQ is a median. Prove that: BC2 = 4 (AQ2 - AC2).
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387.The side QR of a square PQRS is produced to T. Prove that: PT2 = RT2 + 2QR × QT.
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Long Answer Type
388.In Fig, AD is the median of ∆ABC and AE ⊥ BC. If BC = a, CA = b, AD = p, AE = h and DE = x. Prove that
(i) (ii) (iii)
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Short Answer Type
389.A girl of height 90 cm is walking away from the base of a lamp-post at a speed of 1.2 m/s. If the lamp is 3.6 m above the ground, find the lenght of her shadow after 4 seconds.
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390.Two right triangles ∆PQR and ∆SQR are drawn on the same side of the hypotenuse QR. If PR and SQ intersect at M such that PM = 3cm, MR = 6cm and SM = 4 cm, find MQ.
Long Answer Type
(ii) 
Short Answer Type
