51.Given two points A and B and a positive real number k. Find the locus of a point P such that ar(ΔPAB) = k.
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52.Show that the line segment joining the mid-points of a pair of opposite sides of a parallelogram divides it into two equal parallelograms.
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53.In an equilateral triangle, O is any point is the interior of the triangle and perpendiculars are drawn from O to the sides. Prove that the sum of these perpendicular line segments is constant.
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54.ΔABC and ΔABD are two triangles on the same base AB. If line segment CD is bisected by AB at O, show that ar (ΔABC) = ar (ΔABD).
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55. ΔABC and ΔABD are two triangles on the same base AB. If line segment CD is bisected by AB at O, show that ar (ΔABC) = ar (ΔABD).
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Long Answer Type
56.
ABCD is a parallelogram whose diagonals intersect at O. If P is any point on BO, prove that
(i) ar(ΔADO) = ar(ΔCDO) (ii) ar(ΔABP) = ar(ΔCBP)
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Short Answer Type
57.In the given figure, ΔABC is right angled at B, and BD is its median. E is the mid-point of BD. If AB = 6 cm, AC = 10 cm, calculate area of ΔBEC.
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Long Answer Type
58.In the given figure, ΔABC is right angled at A and AD is its median. BA is produced to E such that BA = AE. ED is joined. If AB = 6 cm, BC = 10 cm, find ar(ΔBED).
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59.
The medians of ΔABC intersect at G. Prove that
ar(ΔAGB) = ar(ΔAGC) = ar(ΔBGC)
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Short Answer Type
60.Triangles ABC and DBC are on the same base BC with vertices A and D on opposite sides of BC such that ar (ΔABC) = ar(ΔDBC). Show that BC bisects AD.
Short Answer Type
Long Answer Type
