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

Simple but powerful inequality

A very simple but powerful #inequality you must know at #school level! This can be simply proved by the fact that the square of a real number is always non-negative.

 #Solution: https://t.me/PrimeMaths/33

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A very simple but powerful #inequality you must know at #school level! #Solution: https://t.me/PrimeMaths/33 #Mathematics #Algbera #HighSchool #learning #PrimeMaths #Math #Square

A post shared by Prime Maths (@prime.maths) on Jul 7, 2020 at 7:19am PDT

incentre of Orthic Triangle:

In ∆ABC, let D, E, F denote the feet of the #altitudes from A, B and C respectively. The DEF is called the #orthic #triangle of ABC. Prove that H is the #incenter of △DEF.

#Solution: https://t.me/PrimeMaths/38

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In ∆ABC, let D, E, F denote the feet of the #altitudes from A, B and C respectively. The DEF is called the #orthic #triangle of ABC. Prove that H is the #incenter of △DEF. #PrimeMaths #geometry #maths #mathematics #Solution: https://t.me/PrimeMaths/38

A post shared by Prime Maths (@prime.maths) on Jul 10, 2020 at 8:31am 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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