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Frank Ayres First Year College Math (Schaum's Outline). I have/like the original 1958 edition (easy to get used), but the newer edition with co-author is probably OK, also. https://www.amazon.com/Theory-problems-first-college-mathematics/dp/B0007DPVM2 Since it is a review, it is written economically and clearly. Directed at the student as the customer, not ...


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That book gets ripped pretty hard on Amazon. The Dover texts by Trudeau and Chartrand are supposedly easier and friendlier, per reviews. And will be cheap, since Dover. If you want to develop familiarity and speed, I would certainly not eschew (i.e. I would do) problems that are repetitive. You'll get more practiced at the concept. Also more practiced at ...


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I have this book. A lot of the problems are pretty similar and there are a lot in there. Normally, I'm in favor of doing all the exercises (since you get faster as you go). But I really don't think that quantity of drill is required for a strong student, especially since this is a course that some people still eschew (not taking any proofs class). Maybe ...


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Firstly, congratulations for taking on this task. Of course it is very important to actually complete problems, rather than just read the notes. I would say that completing the odd numbers is a sensible compromise - you can go back and complete the even questions at a later date for more practice or revision. Good luck!


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So some great books on geometry and written for middle/high schoolers are those written by Kiselev and translated to English by Alexander Givental. The textbooks are "Planimetry" and "Stereometry" respectively. Maybe try taking a look in either of those books and see if there is something that suits you? Here's a link to the first. https:/...


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I took an undergraduate course in "advanced planar geometry" in preparation for secondary teaching. It was from the text by Isaacs, "Geometry for College Students (Pure and Applied Undergraduate Texts)" and is available for purchase here. There are also less upstanding ways to obtain this text. It appears to cover all the topics you've ...


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@MatthewDaly's mention of The Secrets of Triangles reminded me of the just released A Cornucopia of Quadrilaterals, which I've been reading. (Alsina, Claudi, and Roger B. Nelsen. Vol. 55. American Mathematical Soc., 2020.) For example, for a bicentric quadrilateral (cyclic and tangential) of side lengths $a,b,c,d$ and angles $A,B,C,D$: \begin{align*} a + c &...


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In my (lack of) experience, the second class in Euclidean geometry is actually an undergraduate course that seems to be often called College Geometry. And, yeah, there are so many fascinating topics there that are accessible to gifted HS students that don't really measure up to other topics when it comes to career and college readiness, but they were the ...


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I wonder if you'd enjoy an older textbook on Solid Geometry. (The only ones I've ever seen are quite old. Maybe there's newer.) But that may not address the particular topics you mentioned.


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I recommend either Excursions in Geometry by Ogilvy or Geometry Revisited by Coxeter and Greitzer. Both are cheap too.


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A quick Google search returned the following texts based on key words from your posting: rational circle, Euler line, geometry textbook. Based on skimming the contents and prefaces, I think they are good chance to match your desires: A Beautiful Journey through Olympiad Geometry, Stefan Lozanovski, 2016 https://www.olympiadgeometry.com/the-book.html ...


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Use of color definitely can be helpful in learning mathematics. Presentation matters. I have given up on texts using an awful font: if learning the idea requires 95% of my brainpower, and deciphering the bad presentation uses up 10% of my brainpower, it makes the difference between learning and not learning. That said, using color intelligently requires ...


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Part of the cost of a printed book is the cost of paper, printing, and binding (PPB). These costs can be lowered with economies of scale when you are printing a lot of copies. Many of the costs are basically costs to set up for a run, while the incremental cost of printing one more book is small. (This is for traditional printing, not print-on-demand.) Upper-...


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