It's a deal. There are many graphics programs and simple drawings like the triangle I do with the Windows Paint. That gives me a bitmap. Likewise, there are many graphics format converters, even as shareware. I use Adobe Photoshop (not shareware!). Simply copy the bitmap into Photoshop and export is as a GIF. If I want a transparent GIF (i.e., one color in the picture selected as transparent), I usually have to do it twice - the Photoshop does not let me do it in one step. First, I export as a normal GIF. Then I load this GIF file and export it as a transparent GIF.

To use subscripts, indexes, and greek symbols, you have to type your message as a kind of HTML code. For example, the triangle symbol is the capital greek delta: <font face="symbol">D</font>ABC, but you have to use rectangular parenthesis - DABC. Partial derivative is <font face="symbol">¶</font>P/<font face="symbol">¶</font>x - ¶P/¶x. See the Windows accessory/system tool Character Map. Likewise, subscripts or superscripts are x_i or x⁵ - xi or x5. See the HTML reference help to the right of the window wher you type. It has some pitfalls: If you use <CODE> ... </CODE> and do not use line breaks, the message text does not wrap. The <ENTER> key or the HTML code <BR> do the line breaks.

I admit that your proof is simpler, you should have included it the first time. I guess I was stubbornly looking for some triangles with the same altitudes. When trying to read your construction, I encountered things like constructing a point that already existed, constructing a circle for no other purpose than to double a line segment and than using its length somewhere else, etc.

Regards, Vladimir