Geometry Proof

Bob · 2016-08-12 19:43:19

hi basketballstar123

This wasn't my proof, but here's how I know this to be true. The circle centred on G defines the point H. AHB is 90 at it is the angle at the circumference subtended by the diameter AB **. AB is parallel to CD so angle AHB = HBD (use x + y = 90).

Bob

** http://www.mathisfunforum.com/viewtopic.php?id=17799 post #6

dazzle1230 · 2016-08-14 02:05:39

Is there a way to solve this problem by making ABP a medial triangle?

thickhead · 2016-08-14 16:27:40

Last edited by thickhead (2016-09-01 20:18:28)

dazzle1230 · 2016-09-01 08:39:32

Also, what is M and J?

Last edited by dazzle1230 (2016-09-01 08:40:22)

thickhead · 2016-09-01 15:37:49

phrontister wrote:

Good luck, Bob!
Yes, I thought there should be an easier way, too...as there was with this one, with ΔPEB being 1/3rd of ΔPCA.
Here's another diagram, with another property revealed by Geogebra: ie, CL = LP = HM. But again, I don't know how to use that info.
This time I've marked some of the equal-length lines.

This was the digram I was referring to.

dazzle1230 · 2016-09-03 05:01:08

How do you know that AB=LM without using geogebra?

phrontister · 2016-09-03 11:20:41

Hi dazzle1230;

How do you know that AB=LM without using geogebra?

AB & LM are opposite sides of rectangle ABML (from post #24):

Proof that H is CD's midpoint:
(i) ABML is a rectangle (tangent perpendicular to radius theorem [see 'Tangent Angle' at bottom of page here] for points A & B; AB is parallel to CD [see post #1]; AE extends to L)

Last edited by phrontister (2016-09-04 02:19:59)

dazzle1230 · 2016-09-04 08:16:43

then wouldnt we have to prove that there are perpendicular lines?

phrontister · 2016-09-04 11:44:40

With parallel lines (AB and CD in this case), a line that is perpendicular to one (eg, as a tangent radius) is perpendicular to both.

ET ag · 2017-03-30 12:22:56

I like how this was a discussion about a certain proof, and then it somehow transformed about a discussion of a movie.

bobbym · 2017-03-30 14:49:30

Hi;

This forum is kind of informal and friendly. Ask a question and help comes, it is that easy.

There really was only a bit about that movie, this thread is stuffed, I mean stuffed with geometry.

iamaditya · 2017-03-30 19:05:35

There are no posts about movie, I see.

zapyourtumor · 2017-04-19 04:18:33

I tried the approach of defining point M as the midpoint of AB and point N as the midpoint of CD, and also tried the approach of defining N as a point on CD such that AM=MN, effectively working backwards, but it didn't work...

If ANB = 90, the midpoint of the hypotenuse, M, will also be the circumcenter of ANB, therefore AM=BM=NM. I don't know how to prove that ANB is a right triangle.
I also used some arc lengths and tangents to prove that angle BDP is congruent to ABP

zapyourtumor · 2017-04-19 04:20:09

iamaditya wrote:

There are no posts about movie, I see.

A space odyssey, first page

Bob · 2017-04-19 06:43:20

hi zapyourtumor

Welcome to the forum.

This is a long thread and there's at least one other on this question. The answer to your question is in there somewhere; you just need to go back to the early posts. I recommend you use my labelling rather than using M and N. Then you'll find the answer.

Bob

Math Is Fun Forum

#26 2016-08-12 19:43:19

Re: Geometry Proof

#27 2016-08-14 02:05:39

Re: Geometry Proof

#28 2016-08-14 16:27:40

Re: Geometry Proof

#29 2016-09-01 08:39:32

Re: Geometry Proof

#30 2016-09-01 15:37:49

Re: Geometry Proof

#31 2016-09-03 05:01:08

Re: Geometry Proof

#32 2016-09-03 11:20:41

Re: Geometry Proof

#33 2016-09-04 08:16:43

Re: Geometry Proof

#34 2016-09-04 11:44:40

Re: Geometry Proof

#35 2017-03-30 12:22:56

Re: Geometry Proof

#36 2017-03-30 14:49:30

Re: Geometry Proof

#37 2017-03-30 19:05:35

Re: Geometry Proof

#38 2017-04-19 04:18:33

Re: Geometry Proof

#39 2017-04-19 04:20:09

Re: Geometry Proof

#40 2017-04-19 06:43:20

Re: Geometry Proof

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