Proving Concurrent Segments in a Triangle-Circle Configuration

In summary, we are given a triangle ABC and a circle intersecting each side at two points, and we need to prove that if certain segments are concurrent, then other segments are also concurrent. This will involve using the equation (AF/FC)*(CD/DB)*(BE/EA)=1, and possibly the SAS method.
  • #1
smokinjoe129
1
0

Homework Statement



Given a triangle ABC and a circle intersecting each side of ABC at two points( intersects AB at E and E', BC at D and D', and AC at F and F') Prove that if the segments AD, BF, and CE are concurrent, then the segments AD', BF', and CE' are concurrent. I am just looking for little hints.

Homework Equations


(AF/FC)*(CD/DB)*(BE/EA)=1
This is in Euclidean.

The Attempt at a Solution


I have drawn the picture, but I am drawing a blank at how to start it, other than I know (AF/FC)*(CD/DB)*(BE/EA)=1
 
Physics news on Phys.org
  • #2
is involved. I am not sure if I should use SAS or something else. Is there any little hint I am missing?
 

1. What is abstract geometry?

Abstract geometry is a branch of mathematics that deals with the study of geometric shapes and figures without using specific numerical measurements. It focuses on the properties and relationships between geometric objects, rather than their specific measurements.

2. What is a geometry proof?

A geometry proof is a logical argument that uses definitions, axioms, postulates, and previously proven theorems to show that a statement or theorem is true. It is a step-by-step process that follows a set of rules to justify the validity of a geometric statement.

3. What is the purpose of an abstract geometry proof?

The purpose of an abstract geometry proof is to provide a logical and rigorous justification for a mathematical statement or theorem. It allows mathematicians to show that a statement or theorem is true in all cases, not just through specific examples.

4. What are the basic elements of an abstract geometry proof?

The basic elements of an abstract geometry proof include statements, reasons, and diagrams. The statements are the given information and the reasons are the justifications for each step in the proof. Diagrams are often used to visually represent the given information and aid in the understanding of the proof.

5. How do you write an abstract geometry proof?

To write an abstract geometry proof, you first need to identify the given information and the statement or theorem that needs to be proven. Then, you must use definitions, axioms, postulates, and previously proven theorems to logically justify each step. Finally, you must conclude with a statement that summarizes the proof and shows that the original statement or theorem is true.

Similar threads

Prove the Extended Law of Sines
    • Calculus and Beyond Homework Help
Replies
1
Views
966
MHB Find length that minimizes the perimeter
    • General Math
Replies
1
Views
663
Prove Homothetic Triangles Concurrent: Ceva's Theorem
    • Precalculus Mathematics Homework Help
Replies
1
Views
2K
MHB Geom Ch: Prove $AB=x^3$ Given $\triangle ABC$ & $\triangle AEF$
    • General Math
Replies
1
Views
842
MHB Proving Equality of Angles in an Acute Triangle
    • General Math
Replies
4
Views
765
Medians of an Isosceles triangle
    • Calculus and Beyond Homework Help
Replies
1
Views
3K
MHB Acute Triangle ABC: Point P and Line Intersections Formula
    • Math POTW for Secondary and High School Students
Replies
1
Views
805
Euclidean and non Euclidean geometries problems
    • Precalculus Mathematics Homework Help
Replies
4
Views
3K
Find the ratio of two line segments in a triangle
    • Precalculus Mathematics Homework Help
Replies
1
Views
2K
MHB Analytic geometry proof with triangle.
    • General Math
Replies
3
Views
1K

Hot Threads

Recent Insights

Back
Top