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reference and a new citation is needed. I am also concerned about the veracity of the formulae, although I am pretty sure that they are essentially correct. The problem seems to be that these formulae appear to be directly related to the diagram and the relative positions of the two circles, so they may not be the general formulae that is implied by the section. --
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Well the current diagram is from me. However as far as I recall I neither wrote the text nor looked at its sources, but just created the diagram based on the existing text and/or an older png drawing. I don't/didn't spot a mistake in general at first glance and i can only access the first page of the
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not belong there? It shows constructing an orthogonal circle which is done after the tangent point T has been constructed. That doesn't match with the caption and it confuses a bit with the description of the construction using Thale's theorem rather than adding to it. It seems it would be better to
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The section giving formulae for the points of intersection of the outer tangent lines to two circles has some problems. The reference given was present when the section was much smaller and contained no formulae, and as such was okay as a citation. However, none of the formulae are mentioned in this
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There is something wrong in the subsection "Geometrical constructions" of section "Tangent lines to one circle". When the text explains that Thales' theorem may be used to construct the tangent lines, the point Q is defined as "the midpoint of the line segment OP". However, in the corresponding
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source currently, hence i'm not clear whether it does source the given formula in detail or not.But of course inin case that the given source is indeed not sufficient an additional should be provided. That aside i'd opt for keeping the formula as long as no error is spotted.--
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While the reference might not mention the formulae that are shown, the formulae are still valid. Can we just remove the reference? I feel like leaving it there with the "validation failed" can cause readers to think there's something wrong with them when there isn't.
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The section
Tangent lines to two circles starts with the assertion the in general two circles have four common tangents. Actually, there are either 0, 2 or 4 lines depending on whether one is inside the other, the circles intersect, or they lie outside each
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Please check the following formula: gamma=atan((y2-y1)/(x2-x1)). I didn't try it for all possible geometries but it seems that it should read as follows: gamma=-atan((y2-y1)/(x2-x1)).
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You are right! There is a missing sign for gamma. I just tried the formula an was confused that it gave wrong results. With the sign it works.
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diagram Q is obviously not at the mentioned midpoint. (Actually, the figure description gives a different definition for Q.)
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remove it. Then a picture of the described construction can be added if it is made.
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Could these be rolled into a single section, with a single diagram?
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Diagram mismatch for Thales' theorem tangents construction
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