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**bob bundy****Administrator**- Registered: 2010-06-20
- Posts: 8,696

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

Children are not defined by school ...........The Fonz

You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei

Sometimes I deliberately make mistakes, just to test you! …………….Bob Bundy

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**dazzle1230****Member**- Registered: 2016-05-17
- Posts: 92

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

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**thickhead****Member**- Registered: 2016-04-16
- Posts: 1,086

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

**{1}Vasudhaiva Kutumakam.{The whole Universe is a family.}(2)Yatra naaryasthu poojyanthe Ramanthe tatra Devataha{Gods rejoice at those places where ladies are respected.}**

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**dazzle1230****Member**- Registered: 2016-05-17
- Posts: 92

Also, what is M and J?

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

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**thickhead****Member**- Registered: 2016-04-16
- Posts: 1,086

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.

**{1}Vasudhaiva Kutumakam.{The whole Universe is a family.}(2)Yatra naaryasthu poojyanthe Ramanthe tatra Devataha{Gods rejoice at those places where ladies are respected.}**

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**dazzle1230****Member**- Registered: 2016-05-17
- Posts: 92

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

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**phrontister****Real Member**- From: The Land of Tomorrow
- Registered: 2009-07-12
- Posts: 4,633

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 radiustheorem [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)*

"The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do." - Ted Nelson

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**dazzle1230****Member**- Registered: 2016-05-17
- Posts: 92

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

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**phrontister****Real Member**- From: The Land of Tomorrow
- Registered: 2009-07-12
- Posts: 4,633

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.

"The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do." - Ted Nelson

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**ET ag****Member**- Registered: 2017-02-22
- Posts: 10

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

If a second was a minute, and a minute was an hour, how many hours would be in one day? (There are multiple answers and they are debatable)

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**bobbym****bumpkin**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606

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.

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**** Always satisfy the Prime Directive of getting the right answer above all else.**

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**iamaditya****Member**- From: Planet Mars
- Registered: 2016-11-15
- Posts: 821

There are no posts about movie, I see.

Practice makes a man perfect.

There is no substitute to hard work

All of us do not have equal talents but everybody has equal oppurtunities to build their talents.-APJ Abdul Kalam

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**zapyourtumor****Member**- Registered: 2017-04-19
- Posts: 3

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

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**zapyourtumor****Member**- Registered: 2017-04-19
- Posts: 3

iamaditya wrote:

There are no posts about movie, I see.

A space odyssey, first page

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**bob bundy****Administrator**- Registered: 2010-06-20
- Posts: 8,696

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

Children are not defined by school ...........The Fonz

You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei

Sometimes I deliberately make mistakes, just to test you! …………….Bob Bundy

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