Prove AB=2CE | Geometry Problem

  • Thread starter Thread starter rushikesh
  • Start date Start date
  • Tags Tags
    Geometry
AI Thread Summary
To prove that AB=2CE, start by calculating the angles of triangle CDE in terms of angle BAC, given that line AC is parallel to DE. Use the sine formula to establish a relationship between the lengths |CE| and |CD|. The varying angle BAC will affect the angles of triangle CDE, but they remain interrelated. This relationship allows for the necessary proof to be constructed. The discussion emphasizes the importance of understanding angle relationships in geometry.
rushikesh
Messages
20
Reaction score
1
In the figure attached, I have to prove AB=2CE given that: line AC is parallel to DE and angles as mentioned in the figure. Can anyone please help me to prove the same?
 

Attachments

  • clip_image002.jpg
    clip_image002.jpg
    4.6 KB · Views: 436
Physics news on Phys.org
Calculate angles of the triangle ##CDE## in terms of ##\angle BAC## Then use the sine formula to relate ##|CE|## to ##|CD|##
 
∠BAC can vary and so will the angles of the Triangle CDE
 
rushikesh said:
∠BAC can vary and so will the angles of the Triangle CDE

They can. But they're related, so you can express one in terms of the other.
 

Thread 'Finding the number of ways to arrange identical balls in a circle (3 different colors)'

I tried to combine those 2 formulas but it didn't work. I tried using another case where there are 2 red balls and 2 blue balls only so when combining the formula I got ##\frac{(4-1)!}{2!2!}=\frac{3}{2}## which does not make sense. Is there any formula to calculate cyclic permutation of identical objects or I have to do it by listing all the possibilities? Thanks
View full post »

Thread 'Greatest possible value of a constant in polynomial'

Since ##px^9+q## is the factor, then ##x^9=\frac{-q}{p}## will be one of the roots. Let ##f(x)=27x^{18}+bx^9+70##, then: $$27\left(\frac{-q}{p}\right)^2+b\left(\frac{-q}{p}\right)+70=0$$ $$b=27 \frac{q}{p}+70 \frac{p}{q}$$ $$b=\frac{27q^2+70p^2}{pq}$$ From this expression, it looks like there is no greatest value of ##b## because increasing the value of ##p## and ##q## will also increase the value of ##b##. How to find the greatest value of ##b##? Thanks
View full post »

Similar threads

Vector addition and parallel vectors problem
Replies
6
Views
1K
Find Side AB: Calculate Using m & n Ratios
Replies
7
Views
3K
Simple geometry problem -- Find the perimeter of the triangle ABC
Replies
7
Views
3K
1st year high school geometry proof
Replies
14
Views
1K
B A triangle problem: Prove that |AC|+|AB|=|PR|+|PQ| given some constraints
Replies
13
Views
2K
Suggestions for HS geometry book (proofs)
Replies
14
Views
1K
Proving that ABE is a Straight Line: Vector Method
Replies
11
Views
5K
Proving one equation, cyclic in variables ##a,b,c##, to another
Replies
4
Views
2K
Prove that ##AE=2BC## -Deductive Geometry
2
Replies
52
Views
4K
Angles inscribed in circles part 1
Replies
6
Views
2K

Hot Threads

Recent Insights

Back
Top