Proving Perpendicularity of FE & AB in a Semicircle

  • Thread starter Thread starter Saad
  • Start date Start date
AI Thread Summary
To prove that line FE extended is perpendicular to diameter AB in a semicircle, it is essential to utilize the properties of right triangles ACB and ADB, which have right angles at points C and D on the arc. The proof can be simplified by applying analytical geometry rather than classical methods, which may involve identifying congruent triangles. The intersection point E of lines AD and BC plays a crucial role in establishing the relationship between the angles formed. By demonstrating that the angles at E are complementary, the perpendicularity of FE to AB can be confirmed. This approach effectively clarifies the geometric relationships within the semicircle.
Saad
Messages
18
Reaction score
0
AB is the diameter of a semicircle. Points C and D are ANY two points on the arc of the semicircle. AD and BC intersect at E. AC and BD are extended to meet at F. Prove that FE extended is perpendicular to AB.

I need any help possible because i have no idea of how to solve this proof problem! pleasezzzzzzzzzzzzz
 
Physics news on Phys.org
The assertion is fairly easy to prove if you rephrase it in the terms of analytical geometry.
It looks difficult to prove it by "classical" means (i.e. identifying congruent triangles and suchlike)
 
Use the fact that triangles ACB and ADB are right triangles with right angle at C and D.
 
Thread 'Collision of a bullet on a rod-string system: query'

Thread 'Collision of a bullet on a rod-string system: query'

In this question, I have a question. I am NOT trying to solve it, but it is just a conceptual question. Consider the point on the rod, which connects the string and the rod. My question: just before and after the collision, is ANGULAR momentum CONSERVED about this point? Lets call the point which connects the string and rod as P. Why am I asking this? : it is clear from the scenario that the point of concern, which connects the string and the rod, moves in a circular path due to the string...
View full post »

Similar threads

Book plots position & force on the same graph, still gets right answer
Replies
8
Views
810
To find the distance of a horizontally suspended rod from a ceiling
Replies
2
Views
1K
To what extent does this system behave as a pendulum?
Replies
1
Views
837
To find the center of gravity of a particular quadrilateral
Replies
12
Views
3K
Uniform Motion in 2D - A man chasing a bus
Replies
20
Views
1K
Prove the Extended Law of Sines
Replies
1
Views
2K
Projectile motion with ##N## bounces on the ground
Replies
21
Views
944
To find the resultant of forces on a lamina
Replies
5
Views
3K
MHB Problem #422: Four Non-Negative Real Numbers and a Unique Condition
Replies
1
Views
2K
MHB Find All Possible Values of $AD$ in Cyclic Quadrilateral
Replies
1
Views
1K

Hot Threads

Recent Insights

Back
Top