In the given Fig, DE || BC and DE divides ∆ABC in two parts such that ar (∆ADE) = , prove that
Solution not provided.
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Short Answer Type
392.In the given fig. DE||BC and AD: DB = 3:4 Find (i)
and (ii)
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393. In ∆ABC, if AD is the median, show that AB2 + AC2 = 2 (AD2 + BD2).
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394.ABCD is a square, F is the midpoint of AB and E is a point on BC such that BE is one-third of BC. If the area of ∆FBE is 108 cm2, find the length AC.
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Long Answer Type
395.P is a point in the interior of rectangle ABCD. If P is joined to each of the vertices of the rectangle. (A) Prove that PB2 + PD2 = PA2 + PC2. (B) If PA, PB and PC are 3 cm, 4 cm and 5 cm respectively, find the length of PD.
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396.Prove that three times the sum of the squares of the sides of a triangle is equal to four times the sum of the squares of the medians of the triangle.
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Short Answer Type
397.A point D is on the side BC of an equilateral ∆ABC such that Prove that AD2 = BCD2.
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398.P is the mid-point AD of a parallelogram ABCD. The straight line BP intersect the diagonal AC at R and CD produced to Q. Prove that 2BR = OR.
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399.In a ∆ABC, D and E are points on sides AB and AC respectively such that BD = CE. If ∠B = ∠C. Show that DE || BC.
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400.In ∆ABC, AD ⊥ BC and AD2 = BC × DC, prove that ∠BAC = 90°.
Long Answer Type
Short Answer Type
, prove that 
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