I shall take a look at that page.

]]>But they are all in dictionary.com

Bob

ps. The inscribed circle page is done.

]]>http://dictionary.reference.com/browse/homomorphism?s=t

B

]]>And besides, you cannot expect a suffix to recognize mathematical terminology, can you? I doubt it would recpgnize "homomorphism" and the like. xD

]]>OK. I'll do inscribed (and maybe exscribed* too) and start to learn about inversion.

Bob

*My spell checker says that's wrong but all my books spell it that way. Maybe 'escribed' ?

]]>While I'd love to do that, I don't think I'll have time in the near future.

Oh and yes, inscribed circles are a must!

]]>Glad you like them. Would you like to add your inversion post ?

I probably need to add the inscribed circle to my list.

Bob

]]>These threads are a fantastic idea! Nice work.

An intersting fact about the Nine Point Circle (I also know it under the name of Euler's Circle) is that when you apply inversion around the Nine Point Circle, the circumcircle gets mapped into the incircle and vice versa!

]]>Theorem.

There is a circle that goes through all of the points D, E, F; G, H, I; J, K, L.

Proof.

Construct the circumcircle of DEF. (I have shown the centre, M, but left out the construction lines to avoid cluttering the diagram.)

As F and D are the midpoints of AB and BC, FD//AC.

As F and J are the midpoints of AB and AN, FJ//BH

But AHB is 90. => JFD is also 90.

We already know that D and F lie on a circle; now we know that J also lies on that circle as JD subtends an angle of 90 at the circumference of the circle. (In fact JD is a diameter.) This follows from one of the angle properties of a circle which you will find here: http://www.mathisfunforum.com/viewtopic.php?id=17799

Similarly K and L will lie on this circle.

JGD is 90. => G is also on this circle.

Similarly H and I will lie on this circle.

Bob

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