Open study

is now brainly

With Brainly you can:

  • Get homework help from millions of students and moderators
  • Learn how to solve problems with step-by-step explanations
  • Share your knowledge and earn points by helping other students
  • Learn anywhere, anytime with the Brainly app!

A community for students.

I am trying to solve the following problem, and I have a solution which I don't understand, can you help me? "Show that in a triangle the perpendiculars drawn from the vertices are concurrent. "

Mathematics
See more answers at brainly.com
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

Get this expert

answer on brainly

SEE EXPERT ANSWER

Get your free account and access expert answers to this and thousands of other questions

Here is the solution that I don't understand
1 Attachment
  • phi
We start with a given: 2 of the perpendiculars (AD and BE) meet at point O now show that the third perpendicular also meets at point O i.e. if the line segment CO extended to side AB (at point F) is perpendicular to AB then all three perpendiculars meet at O Does that make sense?
Let me read it just a sec

Not the answer you are looking for?

Search for more explanations.

Ask your own question

Other answers:

This line can you state it in a better way, I don't get it "if the line segment CO extended to side AB (at point F) is perpendicular to AB then all three perpendiculars meet at O "
OK, I got it... right, you are right, what next?
  • phi
The 3rd perpendicular starts at vertex C. We can draw a line CO (C to O). if we continue, CO intersects the third side AB at F. Now if it turns out that COF is perpendicular to AB, then it is the perpendicular, and it goes through O, the same point as the other 2 perpendiculars
So we have to show that if the line CO is extended, and at the point where it meets AB it turns out to be perpendicular, then we are done right?
  • phi
yes. And the proof relies on vectors, and the fact that the dot product of two vectors that are perpendicular = 0
What is the need of that constant l in the equation \(la.(c−b)=0\)
  • phi
good question. It is obviously true, but irrelevant. I would just claim a dot (c-b)= 0
  • phi
Maybe they want to say that AO is too short (i.e. it does not reach the other side), but that we can scale it so that it does.
  • phi
but vectors do not have to "intersect"
OK
  • phi
I assume that relabeling OA as a, etc makes sense. Do you see how BC= c - b (where all 3 are treated as vectors)?
  • phi
Personally, I always "think" vector addition BC+B= c (using head to tail to add), and then rearrange the vectors to get the difference.
  • phi
*b (not B)
OK, so I will be going through the solution, and try to understand it, and if I find any problem, I will post it here. Please come again if you find a new post made on this problem :)
  • phi
roger that.
Thanks a lot
OK, its clear thank you! I wish I could provide you more medals. It's rare that someone digs in the unanswered questions, like you..

Not the answer you are looking for?

Search for more explanations.

Ask your own question