In this pdf you will get all the solved problem from the exercise 20. Before going through the solutions you are advised to first try the problem yourself. If you get stuck, seek help from the solutions. Don't copy blindly. If you have any query, comment below.
Solved Problems for Indian Statistical Institute (B. Math and B. Stat), Chennai Mathematical Institute, JEE Main & Advance ( IIT ) and for Olympiads ( RMO and INMO ). Get Solved problems for boards ( CBSE and ISC Mathematics Papers) along with board papers.
Showing posts with label geometry. Show all posts
Showing posts with label geometry. Show all posts
Thursday, May 28, 2020
Class IX West Bengal Board Ganit Prakash Chapter 20 Solutions- Co-ordinate Geometry
Class IX West Bengal Board Ganit Prakash Chapter 20 Solutions - Coordinate Geometry
Sunday, April 19, 2020
Can You Solve The 5 Circles inside the square Problem?
Five circles with the same radius are placed inside a square, whose sides are not known. The radius of the circle is given. The problem is to find the side of the square. Four circles are placed inside the square at the four corners in such a way that the sides of the square are tangents to the circle. The fifth circle is place between the four circles, such that it touches the four circles externally.
Watch the video for the solution
Watch the video for the solution
Saturday, February 8, 2020
A very interesting problem from Indian Statistical Institute: Geometry
This problem, requires some knowledge of a regular polygon. Only the elementary properties is required. If you don't know anything about regular polygons, just google it! Lot of thinking is required to solve this problem. A very good problem where the calculations are minimal but the logical part is required throughout. Check the full video for the solution and share your views about the problem.
Wednesday, January 29, 2020
An interesting property of cyclic quadrilateral.
In a cyclic quadrilateral the product of its diagonals is equal to the sum of the products of it's opposite sides. Watch the full video for the proof.
Sunday, September 8, 2019
Sunday, September 28, 2014
Geometry Inequality
Prove
that in any quadrilateral, the sum of the diagonals is greater than
the half of its perimeter.
Consider
the quad. In the above diagram. Let E be the point of the
intersection.
Now, AE+EB
> AB
EB+EC
> BC
AE+ED
> AD
EC+ED
> DC (Using Triangle Inequality)
Adding
the above four inequalities we get
2(AE+EC+EB+ED)
> AB+BC+AD+DC
=>
AC + BD > ½(AB+BC+AD+DC)
Thus
sum of the diagonals is greater than the half of its perimeter Q.E.D
In
any triangle four times the sum of its medians is greater than 3
times its perimeter.
We
know that difference of any two sides of a triangle is less than the
third side (prove it)
In
triangle ABE,
AE
> AB-BE
In
triangle ACE,
AE
> AC-CE
Adding
above two inequalities we get,
2AE
> AB + AC -(BE+CE)
=>
AE > ½(AB+AC-BC)
=>
4AE > 2(AB+AC-BC).........(1)
Similarly,
4BD
> 2(AB+BC-AC).............(2) and 4CF > 2(AC+BC-AB)........(3)
Adding
(1),(2) and (3) we have,
4(AE+BD+CF)
> 2(AB+AC-BC+AB+BC-AC+AC+BC-AB)
=>
4(AE+BD+CF) > 2(AC+AB+BC)
=>
sum of the lengths of the medians is greater than half the perimeter
We
can strengthen the inequality by using the fact that the point 'O'
divides the medians AE,BD,CF internally in the ration 2:1
Therefore,
OD:OB = 1:2
=>
(OB+OD):OB = (1+2):2
=>
BD:OB=3:2
=>
OB = 2/3 BD........(a)
Similarly,
OC = 2/3 CF.........(b) and OA = 2/3 AE.......(c)
Now
in triangle OBC, OB+OC> BC
=>2/3(BD+CF)>BC
[using (a) and (b)]
=>
2(BD+CF)>3BC
Similarly,
2(CF+AE)>3AC and 2(BD+AE)>3AB
Adding
the last three inequalities we get 4(AE+BD+CF) > 3(AB+BC+CA)
In the triangle ABC, AE,BD and CF are the medians where O is the point of there intersection
Labels:
10th Grade,
cbse,
geometry,
ICSE,
X
Monday, May 26, 2014
Tuesday, May 6, 2014
Coordinate Geometry
Solved Problems on Coordinate Geometry for 10th grade. Problems based on distance formula, section ratio formula
Friday, May 2, 2014
GEOMETRY Thales Theorem or Basic Proportionality Theorem Solved Problems
Solved Problems on Thales Theorem useful for students of 10th grade of CBSE and ICSE and other state board. This material is also useful for the preparation of Regional Mathematics Olympiad. Basic Geometry is a pre-requisite for any Olympiad.
Monday, June 6, 2011
Model Paper
Model Paper for B.Sc Maths Hons. 1st year students from various topics like algebra,geometry and analysis ISC Board Maths paper for the last 5 years is also available with sample papers and guess papers visit http://kolkatamaths.yolasite.com/board-papers.php ISC maths paper for 2011,2010,2009,2008,2007 and CBSE class XII Maths paper for previous year is also available.
Tuesday, April 26, 2011
Problems for WBJEE and AIEEE
MCQ and Short Type Questions for various topics ( relation, functions, derivative, matrices, determinants, trigonometry, inverse, circular Co-ordinate, geometry, two-dimension, tangent, normal) Download
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