MHB Prove Quadrilateral ABCD Perimeter $\geq (4+2\sqrt 2)S$

  • Thread starter Thread starter Albert1
  • Start date Start date
  • Tags Tags
    Convex
Albert1
Messages
1,221
Reaction score
0
A convex quadrilateral ABCD with area $S^2$ , prove the sum of its perimeter and two diagonal lines $\geq (4+2\sqrt 2)S$
 
Last edited:
Mathematics news on Phys.org
Albert said:
A convex quadrilateral ABCD with area $S^2$ , prove the sum of its perimeter and two diagonal lines $\geq (4+2\sqrt 2)S$
hint:
$Use\,\,area\,\,of \,\,a\,\,triangle=\dfrac {bc\,sin \,A}{2}=---,and\,\, AP\geq GP$
 

Thread 'What Exactly is Dirac’s Delta Function? - Insight'

Insights auto threads is broken atm, so I'm manually creating these for new Insight articles. In Dirac’s Principles of Quantum Mechanics published in 1930 he introduced a “convenient notation” he referred to as a “delta function” which he treated as a continuum analog to the discrete Kronecker delta. The Kronecker delta is simply the indexed components of the identity operator in matrix algebra Source: https://www.physicsforums.com/insights/what-exactly-is-diracs-delta-function/ by...
View full post »

Thread 'Fermat's Last Theorem'

Fermat's Last Theorem has long been one of the most famous mathematical problems, and is now one of the most famous theorems. It simply states that the equation $$ a^n+b^n=c^n $$ has no solutions with positive integers if ##n>2.## It was named after Pierre de Fermat (1607-1665). The problem itself stems from the book Arithmetica by Diophantus of Alexandria. It gained popularity because Fermat noted in his copy "Cubum autem in duos cubos, aut quadratoquadratum in duos quadratoquadratos, et...
View full post »

Thread 'Useless continued fraction for 1'

I'm interested to know whether the equation $$1 = 2 - \frac{1}{2 - \frac{1}{2 - \cdots}}$$ is true or not. It can be shown easily that if the continued fraction converges, it cannot converge to anything else than 1. It seems that if the continued fraction converges, the convergence is very slow. The apparent slowness of the convergence makes it difficult to estimate the presence of true convergence numerically. At the moment I don't know whether this converges or not.
View full post »

Similar threads

MHB Prove Quadrilateral Divider: Equal Area & Perimeter
Replies
4
Views
2K
MHB Geometry Challenge: Prove $\angle ADE=\angle BDC$ in Convex Quadrilateral $ADBE$
Replies
3
Views
965
MHB Find the area of the quadrilateral PQRS
Replies
4
Views
2K
MHB A,B,C,D cocyclic prove AC^2=AB×AD+BC^2
Replies
1
Views
2K
MHB Prove Angle of Diagonals in Quadrilateral is Degrees
Replies
3
Views
1K
MHB How Can the Area of a Quadrilateral Be Bounded by Its Side Lengths?
Replies
4
Views
2K
MHB Minimum Perimeter of a Trapezoid: Find R & P
Replies
5
Views
2K
MHB Dividing a Quadrilateral into Equal Parts
Replies
3
Views
5K
MHB Maximum area of triangle and quadrilateral - given perimeter
Replies
6
Views
7K
MHB Prove $\angle QBR=\angle RSQ$: Geometry Challenge
Replies
2
Views
2K

Hot Threads

Recent Insights

Back
Top