MHB Prove: (AC)² = (AD)² + (AB)·(CD)

  • Thread starter Thread starter Albert1
  • Start date Start date
  • Tags Tags
    Ac
Albert1
Messages
1,221
Reaction score
0
A trapezoid ABCD ,AB//CD ,AD=BC

Prove :

$AC^2=AD^2+(AB).(CD)$
 
Mathematics news on Phys.org
Re: Prove :AC^2=AD^2+(AB).(CD)

Albert said:
A trapezoid ABCD ,AB//CD ,AD=BC

Prove :

$AC^2=AD^2+(AB).(CD)$

View attachment 1596
 

Attachments

  • trapezoid.jpg
    trapezoid.jpg
    19.9 KB · Views: 90

Thread 'Non-orthogonal bases'

Suppose ,instead of the usual x,y coordinate system with an I basis vector along the x -axis and a corresponding j basis vector along the y-axis we instead have a different pair of basis vectors ,call them e and f along their respective axes. I have seen that this is an important subject in maths My question is what physical applications does such a model apply to? I am asking here because I have devoted quite a lot of time in the past to understanding convectors and the dual...
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 '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 »

Similar threads

MHB Simplify a+b+c+d+2(ab+ac+ad+bc+bd+cd)+4(abc+abd+acd+bcd)+8(abcd)
Replies
3
Views
2K
MHB A,B,C,D cocyclic prove AC^2=AB×AD+BC^2
Replies
1
Views
2K
B A triangle problem: Prove that |AC|+|AB|=|PR|+|PQ| given some constraints
Replies
13
Views
2K
MHB Find All Possible Values of $AD$ in Cyclic Quadrilateral
Replies
1
Views
1K
MHB Minimum Perimeter of a Trapezoid: Find R & P
Replies
5
Views
2K
MHB What is the value of Angle BAD in a trapezoid with specific conditions?
Replies
2
Views
2K
MHB Prove Inequality: $\sqrt{ab}+\sqrt{cd}\le \sqrt{(a+d)(b+c)}$
Replies
1
Views
1K
MHB Parallelogram ABCD: Finding AC from PB & PD
Replies
1
Views
1K
MHB Prove Triangle Inequality: AB/MZ + AC/ME + BC/MD ≥ 2t/r
Replies
1
Views
2K
MHB Can You Prove that AC//BD and AF//BE are Parallel in this Geometry Problem?
Replies
1
Views
2K

Hot Threads

Recent Insights

Back
Top