Prove that ME=MC in a Circle Geometry ABCD

  • Thread starter Thread starter Lukybear
  • Start date Start date
  • Tags Tags
    Circle Geometry
AI Thread Summary
ABCD is established as a cyclic quadrilateral with diagonals AC and BD intersecting at right angles at point E. The midpoint M of side CD is identified, and line ME is extended to meet line AB at point N. The goal is to demonstrate that the length of ME equals the length of MC. A solution has been found, indicating that the problem can be resolved effectively. The discussion highlights the geometric properties of cyclic quadrilaterals and the relationships between their segments.
Lukybear
Messages
8
Reaction score
0
ABCD is a cyclic quadrilateral. The diagonals AC and BD intersect at right angles at E. M is the midpoint of CD. ME produced meets AB at N.

Show that ME = MC
 

Attachments

  • Circle Geo Independent.jpg
    Circle Geo Independent.jpg
    11.7 KB · Views: 448
Last edited by a moderator:
Physics news on Phys.org
Lukybear said:
ABCD is a cyclic quadrilateral. The diagonals AC and BD intersect at right angles at E. M is the midpoint of CD. ME produced meets AB at N.

Show that ME = MC

What are your thoughts on how to proceed?
 
Nvm, I've found solution. Thxs.
 

Thread 'Family of lines that are at a distance of 5 from the origin'

I picked up this problem from the Schaum's series book titled "College Mathematics" by Ayres/Schmidt. It is a solved problem in the book. But what surprised me was that the solution to this problem was given in one line without any explanation. I could, therefore, not understand how the given one-line solution was reached. The one-line solution in the book says: The equation is ##x \cos{\omega} +y \sin{\omega} - 5 = 0##, ##\omega## being the parameter. From my side, the only thing I could...
View full post »

Similar threads

Prove that ##AE=2BC## -Deductive Geometry
2
Replies
52
Views
3K
MHB Find All Possible Values of $AD$ in Cyclic Quadrilateral
Replies
1
Views
1K
Vector algebra (proving you have a parallelogram by using vectors)
Replies
7
Views
4K
Parallelogram area (coordinates)
Replies
8
Views
3K
B Proof of Cyclic Quadrilateral AEDT in Circle ABCD
Replies
1
Views
2K
Euclidean and non Euclidean geometries problems
Replies
4
Views
3K
MHB Can You Prove that AC//BD and AF//BE are Parallel in this Geometry Problem?
Replies
1
Views
2K
Ptolemy's Theorem and Cyclic Quadrilateral
Replies
1
Views
4K
How do I prove it is a diagonal?
Replies
9
Views
2K
Finding the diagonal of an irregular quadrilateral
Replies
1
Views
28K

Hot Threads

Recent Insights

Back
Top