# Can Cecil Solve this Gometry Stumper?
**URL:** https://boards.straightdope.com/t/can-cecil-solve-this-gometry-stumper/663662
**Category:** Cecil's Columns/Staff Reports
**Created:** [July 16, 2013, 1:34pm UTC](https://boards.straightdope.com/t/can-cecil-solve-this-gometry-stumper/663662 "2013-07-16T13:34:46Z")
**Posts on this page:** 12
**Page:** 1
### Author:  [@Patch](https://boards.straightdope.com/u/Patch)
#### Post date: [July 16, 2013, 1:34pm UTC](https://boards.straightdope.com/t/can-cecil-solve-this-gometry-stumper/663662/1 "2013-07-16T13:34:46Z")
[In the latest column reprint](http://www.straightdope.com/columns/read/917/can-cecil-solve-this-geometry-stumper), how about including the diagram of the problem Cecil’s trying to solve? I know it was there for the books.
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### Author:  [@tim314](https://boards.straightdope.com/u/tim314)
#### Post date: [July 16, 2013, 3:17pm UTC](https://boards.straightdope.com/t/can-cecil-solve-this-gometry-stumper/663662/2 "2013-07-16T15:17:05Z")
Yeah, it’s scarcely worth reprinting without the image.
**BigT** provided an image in this previous thread. [Geometry problem Jan. 4, 1991 - Cecil's Columns/Staff Reports - Straight Dope Message Board](http://boards.straightdope.com/sdmb/showthread.php?t=632798)
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### Author:  [@don\_t\_ask](https://boards.straightdope.com/u/don_t_ask)
#### Post date: [July 16, 2013, 3:23pm UTC](https://boards.straightdope.com/t/can-cecil-solve-this-gometry-stumper/663662/3 "2013-07-16T15:23:54Z")
Cecil knows fuck all about gometry.
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### Author:  [@Powers](https://boards.straightdope.com/u/Powers)
#### Post date: [July 16, 2013, 8:57pm UTC](https://boards.straightdope.com/t/can-cecil-solve-this-gometry-stumper/663662/4 "2013-07-16T20:57:00Z")
> [@don\_t\_ask](#):
>
> Cecil knows fuck all about gometry.
Then he matches your facility with spelling, I guess.
Powers &8^]
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### Author:  [@John\_W.Kennedy](https://boards.straightdope.com/u/John_W.Kennedy)
#### Post date: [July 16, 2013, 11:56pm UTC](https://boards.straightdope.com/t/can-cecil-solve-this-gometry-stumper/663662/5 "2013-07-16T23:56:18Z")
> [@don\_t\_ask](#):
>
> Cecil knows fuck all about gometry.
F-
Show your work!
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### Author:  [@Hari\_Seldon](https://boards.straightdope.com/u/Hari_Seldon)
#### Post date: [July 17, 2013, 12:11pm UTC](https://boards.straightdope.com/t/can-cecil-solve-this-gometry-stumper/663662/6 "2013-07-17T12:11:45Z")
No Cecil’s geometry is correct at least I assume since without the diagram, I don’t know where to go after step 8. Fortunately, there is no need to go past step 8. Here’s why. At step 8, he claims, correctly, that angle XCE = angle YCE. But that implies that E is on the angle bisector of angle ACE (= angle XCY). But it is well known that the three angle bisectors meet in a point\*, so D is on the angle bisector.
- Why? The angle bisector of the angle at A (i.e. CAB) consists of all points equidistant from AC and AB and the bisector at B consists of the points equidistant from AB and BC. But then D is also equidistant from AC and BC.
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### Author:  [@Hari\_Seldon](https://boards.straightdope.com/u/Hari_Seldon)
#### Post date: [July 17, 2013, 1:42pm UTC](https://boards.straightdope.com/t/can-cecil-solve-this-gometry-stumper/663662/7 "2013-07-17T13:42:37Z")
Looking back on my previous post, I realize that the proof that E lies on the angle bisector of the angle at C is exactly the same as the proof that D does. In fact, E is equidistant from CA (extended) and CB since it is equidistant from CA and AB and also from CB and AB, hence from AC and BC and that is the same argument for D. Of course, it is well known that the three interior angle bisectors meet at a point; the fact adduced here less known.
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### Author:  [@don\_t\_ask](https://boards.straightdope.com/u/don_t_ask)
#### Post date: [July 17, 2013, 1:57pm UTC](https://boards.straightdope.com/t/can-cecil-solve-this-gometry-stumper/663662/8 "2013-07-17T13:57:56Z")
> [@don\_t\_ask](#):
>
> Cecil knows fuck all about gometry.
I wish to withdraw my comment. As **Powers** and **John W. Kennedy** point out I am plainly wrong and Cecil is one of the great minds of modern gometry. Either that or he knows fuck nothing about it.
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### Author:  [@tim314](https://boards.straightdope.com/u/tim314)
#### Post date: [July 18, 2013, 5:17am UTC](https://boards.straightdope.com/t/can-cecil-solve-this-gometry-stumper/663662/9 "2013-07-18T05:17:35Z")
> [@Powers](#):
>
> Then he matches your facility with spelling, I guess.
**don’t ask** was attempting to call attention to the OP’s misspelling.
Unsuccessfully, I guess. 🙂
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### Author:  [@Powers](https://boards.straightdope.com/u/Powers)
#### Post date: [July 18, 2013, 7:07pm UTC](https://boards.straightdope.com/t/can-cecil-solve-this-gometry-stumper/663662/10 "2013-07-18T19:07:52Z")
Yes, I apologize to **don’t ask**. I didn’t catch the reference.
Powers &8^]
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### Author:  [@BigT](https://boards.straightdope.com/u/BigT)
#### Post date: [July 25, 2013, 4:15pm UTC](https://boards.straightdope.com/t/can-cecil-solve-this-gometry-stumper/663662/11 "2013-07-25T16:15:42Z")
> [@tim314](#):
>
> Yeah, it’s scarcely worth reprinting without the image.
>
> **BigT** provided an image in this previous thread. [Geometry problem Jan. 4, 1991 - Cecil's Columns/Staff Reports - Straight Dope Message Board](http://boards.straightdope.com/sdmb/showthread.php?t=632798)
I did indeed, but it’s on a server that keeps having problems, so I’ll repost it.
Hopefully [this one](http://s23.postimg.org/7hvcq7bsb/cecil_triangle_proof.png) will last longer. (The site was one of the first in Google results, so it should be popular.)
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### Author:  [@Irishman](https://boards.straightdope.com/u/Irishman)
#### Post date: [July 25, 2013, 7:04pm UTC](https://boards.straightdope.com/t/can-cecil-solve-this-gometry-stumper/663662/12 "2013-07-25T19:04:58Z")
I’ve been staring at that drawing and working through Cecil’s column, and something is a little off on that drawing. Cecil says
> [@](#):
>
> (2) Triangles EBY and EBZ are congruent (i.e., equal) because of the angle-angle-side theorem. Proof: angle EYB = EZB (both 90), angle EBY = EBZ (given), segment BE = BE.
Looking at the picture, those triangles clearly are not congruent. However, the problem statement says
> [@](#):
>
> Given any triangle ABC, extend the baseline and bisect the interior and exterior angles at A and B. Extend these four new lines until they intersect at D and E.
That problem statement defines EB as the bisector of angle CBZ. Therefore, I have to conclude the drawing is not precise and work from the problem description, not the visual appearance. Doing so, Cecil’s proof works out.
So for anyone playing at home, the point labels are correct and give a visual correlation for the description, but don’t rely on the appearance of the triangles. It was probably a quick sketch, not a precise bisection.