Find the coordinates of a point A, where AB is the diameter of circle whose centre is (2, – 3) and B is (1,4) .
Let us assume the coordinates of point A be (x, y). Mid-point of AB is (2, – 3), which is the... View Article
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Diagonals AC and BD of a trapezium ABCD with AB || DC intersect each other at O. Prove that ar (AOD) = ar (BOC) .
Solution ΔDAC and ΔDBC lie on the same base DC and between the same parallels AB and CD. Ar(ΔDAC) =... View Article
In Fig. X = 62°, XYZ = 54°. If YO and ZO are the bisectors of XYZ and XZY respectively of Δ XYZ, find OZY and YOZ.
∠X = 62°, ∠XYZ = 54° We know that the sum of the interior angles of the triangle is 180°.... View Article
The distributions of below give a weight of 30 students of a class. Find the median weight of a student.
Weight(in kg) 40-45 45-50 50-55 55-60 60-65 65-70 70-75 Number of students 2 3 8 6 6 3 2 Solution:... View Article
In quadrilateral ACBD, AC = AD and AB bisect A (see Fig.) . Show that ΔABC ΔABD. What can you say about BC and BD?
Solution Given AC and AD are equal AC = AD and the line AB bisects ∠A. To Prove ∆ ABC... View Article
Construct the following quadrilateral: Quadrilateral JUMP. JU = 3.5 cm UM = 4 cm MP = 5 cm PJ = 4.5 cm PU = 6.5 cm
Solution The rough sketch of the quadrilateral JUMP can be drawn as follows. (1) ∆ JUP can be constructed by... View Article
In Figure, two chords AB and CD intersect each other at the point P. Prove that : (i) ∆APC ~ ∆ DPB (ii) AP . PB = CP . DP
Given: chords AB and CD intersect each other at the point P. To prove: (i) Δ APC ~ Δ DPB... View Article
A cuboidal vessel is 10m long and 8m wide. How high must it be made to hold 380 cubic metres of a liquid?
Given Length of the cuboidal vessel, l = 10 m Width of cuboidal vessel, b = 8m Volume of cuboidal... View Article
AD is an altitude of an isosceles triangle ABC in which AB = AC. Show that (i) AD bisects BC (ii) AD bisects A.
Solution Given AD is an altitude and AB = AC To Prove (i) AD bisects BC (ii) AD bisects A.... View Article
E is a point on the side AD produced of a parallelogram ABCD and BE intersects CD at F. Show that ΔABE ~ ΔCFB.
Given E is a point on the side AD produced of a parallelogram ABCD and BE intersects CD at F.... View Article
Diagonal AC of a parallelogram ABCD bisects ∠A (see Fig.) . Show that (i) it bisects ∠C also, (ii) ABCD is a rhombus.
(i) it bisects ∠C also, Since ABCD is a parallelogram. ∠BAC = ∠DCA ……………………………(1) [Alternate interior angles are equal] ∠CAD = ∠BCA... View Article
Determine the ratio in which the line 2x + y – 4 = 0 divides the line segment joining the points A(2, -2) and B(3, 7) .
Assume the line 2x + y – 4 = 0 divides line AB joined by the two points A(2, -2) and... View Article
A cuboidal water tank is 6m long, 5m wide and 4.5m deep. How many litres of water can it hold? (1 m3 = 1000 l)
Given Dimensions of the cuboidal water tank l = 6m, b = 5m, h = 4.5m Find out We have... View Article
Prove that if chords of congruent circles subtend equal angles at their centres, then the chords are equal.
Solution Given AB = CD i.e. two equal chords. To Prove AB = CD Proof From ΔAOB and ΔCOD, OA... View Article
A loaded truck travels 14 km in 25 minutes. If the speed remains the same, how far can it travel in 5 hours?
Solution Let distance covered in 5 hours be x km. 1 hour = 60 minutes Therefore, 5 hours = 5×60... View Article
Find the amount of water displaced by a solid spherical ball of diameter (i) 28 cm (ii) 0.21 m (Assume π = 22/7)
Given Diameter = 28 cm Therefore, the radius, r = 28/2 cm = 14cm volume of the solid spherical ball... View Article
Express the linear equations in the form ax + by + c = 0 and indicate the values of a, b and c in each case: 5 = 2x
We have to express 5 = 2x in the form ax + by + c = 0 and indicate the... View Article
07 July 2021: The Hindu Analysis
UPSC Current Affairs Preparation: The Hindu Analysis Watch expert analysis of ‘The Hindu’ dated 07th Jul 2021. Important news and... View Article
World Heritage Convention
World Heritage Convention The World Heritage Convention is an important global conservation instrument. Such international treaties and conventions are very... View Article
Express the linear equations in the form ax + by + c = 0 and indicate the values of a, b and c in each case: x = 3y
We have to express x = 3y in the form ax + by + c = 0 and indicate the... View Article
