Problem based on Angle bisector

If AD is the angle bisector of ∠BAC in the triangle ABC. Show that AB.AC=BD.DC+AD^2.

#Solution https://t.me/PrimeMaths/43

#Geometry #PrimeMaths #Angle #Bisectors

Factorisation of n^5+n^4+1

To show a given expression not a prime we have to simply factor it into at least two factors with each factor greater than 1. Here is a #problem from #NumberTheory which uses this technique of proving not a #prime.
#PrimeMaths

Binomial Coefficients

An elegant problem from #Binomial Coefficients. Try this out or else see our solution.
#Algebra #Mathematics #CBSE #ISC #IIT #ISI #Learning #practicemakesperfect

Solution: https://t.me/PrimeMaths/24

Integration : Properties of Definite Integral

A nice problem form Indian Statistical Institute. 

#Definite #Integral #Integration #Problem #Calculus 

Solution: https://t.me/PrimeMaths/17

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A nice problem form Indian Statistical Institute. #Definite #Integral #Integration #Problem #Calculus Solution: https://t.me/PrimeMaths/17

A post shared by Prime Maths (@prime.maths) on Jun 28, 2020 at 1:43am PDT

Interesting Property of a Trapezium

Prove that the straight line that passes through the point of intersection of the diagonals of a trapezium and through the point of intersection of its non-parallel sides, bisects each of the parallel sides of the trapezium.

Area of a Triangle

Solution:

Geometry: Problem involving orthocentre

ABC  is a triangle with AB = 13; BC = 14 and CA = 15. AD and BE  are the altitudes from A and B  to BC and AC respectively. H is the point of intersection of AD and BE. Find the ratio HD/HB. 

Solution: 

Cone on a Sphere : Geometry

A hollow right circular cone rests on a sphere as shown in the figure. The height of the cone is 4 metres and the radius of the base is 1 metre. The volume of the sphere is same as that of the cone. What is the distance between the centre of the sphere and the vertex of the cone?

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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

Solved Problems: Trigonometry - Angles and Sides of a Triangle.

To get the pdf file visit the page: http://kolkatamaths.yolasite.com/xi-xii.php
File name: Angles and Sides of a Triangle_Loney

Trigonometry: Elimination Problem