411.D and E are points on the sides AB and AC respectively of ∆ABC such that DE is parallel to BC and AD : DB = 4:5. CD and BE intersect each other at F. Find the ratio of the areas of ∆DEF and ∆BCF.
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412.Two right triangles ABC and DBC are drawn on the same hypotenuse BC and on the same side of BC. If AC prove that AP × PC = BP × PD.
413.D is a point on the side BC of ∆ABC. Such that ∠ADC and ∠BAC are equal. Prove that CA2 = DC × CB.
Solution not provided.
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Short Answer Type
414.In a right angled triangle ABC ∠A = 90° and AD ⊥ BC. Prove that AD2 = BD × CD.
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415.In the given Fig, ABCD is a trapezium in which AB is parallel to DC. If AC trisect BD, then prove that CD = 1/2 AB.
145 Views
416.In ∆ABC, if AD is the median, show that AB2 + AC2 = 2 (AD2 + BD2).
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Long Answer Type
417.
In the given Fig., ABC is a right triangle right angled at B. AD and CE are the two medians drawn from A and C respectively. If AC = 5 cm and find the length of CE.
170 Views
418.Prove that the sum of the squares of the sides of a rhombus is equal sum of the squares on its diagonals.
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Short Answer Type
419.
In the given Fig. PA, QB and RC are each perpendicular to AC. Prove that
389 Views
420.
In the given Fig, ∠ACB = 90°, CD ⊥ AB, prove that CD2 = BD . AD.
Long Answer Type
Short Answer Type
find the length of CE.
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