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D, E and F are respectively the mid-points of sides AB, BC and CA of ΔABC. Find the ratio of the area of ΔDEF and ΔABC.

Given D, E and F are respectively the mid-points of sides AB, BC and CA of ΔABC. Find out We... View Article

In ΔABC, AD is the perpendicular bisector of BC (see Fig. 7.30) . Show that ΔABC is an isosceles triangle in which AB = AC.

Solution Given AD is ⊥ the bisector of BC To Prove AB = AC Proof In ∆ABD and ∆ACD BD=DC... View Article

If E, F, G and H are respectively the mid-points of the sides of a parallelogram ABCD, show that ar (EFGH) = 1/2 ar(ABCD) .

Given E, F, G and H are the mid-points of the sides of a parallelogram ABCD respectively. To Prove ar... View Article

Show that if the diagonals of a quadrilateral are equal and bisect each other at right angles, then it is a square.

Given Let ABCD be a quadrilateral and its diagonals AC and BD bisect each other at right angle at O.... View Article

Find the total surface area of a cone, if its slant height is 21 m and diameter of its base is 24 m. (Assume π = 22/7)

Given Slant height, (l) = 21 m Radius = diameter / 2 Radius (r) = 24/2 m = 12m Find... View Article

Solve the following pair of linear equations by the substitution and cross-multiplication methods: 8x + 5y = 9 3x + 2y = 4

Given equations 8x + 5y = 9 …………………..(1) 3x + 2y = 4 ……………….….(2) From equation (2) we obtain the value of... View Article

Prove that the line of centres of two intersecting circles subtends equal angles at the two points of intersection.

Given: Two circles with centre O and O’ circle intersect at P and Q. To prove: ∠OPO’=∠OQO’ Construction: Join OQ, O’P anQ O’Q... View Article

Describe how the two figures below are alike and how they are different. Which box has larger lateral surface areas?

Given Diameter of cylinder = 7 cm Radius of cylinder (r) = 7 / 2 cm Height of cylinder (h)... View Article

A grandfather is ten times older than his granddaughter. He is also 54 years older than her. Find their present ages.

Solution Let the age of granddaughter be x and Let the age of grandfather be 10x. Given that he is 54... View Article

P and Q are any two points lying on the sides DC and AD respectively of a parallelogram ABCD. Show that ar(APB) = ar(BQC) .

Given P and Q are any two points lying on the sides DC and AD respectively of a parallelogram ABCD... View Article

A park, in the shape of a quadrilateral ABCD, has C = 90°, AB = 9 m, BC = 12 m, CD = 5 m and AD = 8 m. How much area does it occupy?

Given A quadrilateral ABCD where ∠C = 90º, AB = 9 m, BC = 12 m, CD = 5 m and... View Article

Observe the following pattern and find the missing numbers. 112 = 121 1012 = 10201 10012 = 1002001 1000012 = 1 …….2………1 100000012 = ……………………..

Solution From the given pattern, we note that the squares of the given numbers have the same number of zeroes before and... View Article

Prove that the sum of the squares of the diagonals of parallelogram is equal to the sum of the squares of its sides.

Let us consider, ABCD be a parallelogram. Construction: Draw perpendicular DE on extended side of AB, and draw a perpendicular... View Article

Diameter of the base of a cone is 10.5 cm and its slant height is 10 cm. Find its curved surface area (Assume π = 22/7)

Given Slant height of cone, (l) = 10 cm Radius = diameter / 2 Radius(r) = (10.5/2)cm = 5.25cm Find... View Article

Draw a circle and two lines parallel to a given line such that one is a tangent and the other, a secant to the circle.

In the above diagram, XY and AB are two the parallel lines. The line segment AB is the tangent at... View Article

AC and BD are chords of a circle which bisect each other. Prove that (i) AC and BD are diameters; (ii) ABCD is a rectangle.

Given: Two chords AC and BD bisects each other i.e OA=OC,OB=OD To prove: In ∆AOB and COB AO=CO ——-[given] ∠AOB=∠COD... View Article

The perpendicular from A on side BC of a Δ ABC intersects BC at D such that DB = 3CD (see Figure) . Prove that 2AB2 = 2AC2 + BC2.

Given: DB = 3CD To prove: 2AB2 = 2AC2 + BC2 Proof: DB = 3CD BC = CD + DB BC = CD + 3CD... View Article

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