一个小的注意直角三角形
A little noticed right triangle
摘要：
给定一个直角三角形ABC，其90度角在A处;考虑三角形O 1 OO 2，其中点O是直角三角形BC的中点（因此也是三角形ABC外接圆的中心），点O 1是三角形AOB的外接圆中心，点O2是三角形AOC的外接圆中心。三角形O 1 OO 2实际上是类似于ABC的直角三角形。在这项工作的早期部分，一些几何公式推导，包括从附近的梯形段的一些长度。在那之后，焦点改变了。我们研究的情况下，ABC是一个勾股三角形，并找到精确的条件下，三角形O 1 OO 2也勾股。文末还提供了数值表。
英文摘要：
Given a right triangle ABC, with the ninety degree angle at A; consider the triangle O1OO2.Where the point O is the midpoint of the hypotenuseBC(and so the center of the triangle ABC's circumcircle), the point O1 being the triangle AOB's circumcenter, and the point O2 being the triangle AOC circumcenter. The triangle O1OO2 is actually a right triangle similar to ABC. In the early part of this work, some geometrical formulas are derived, including some lengths of segments from a nearby trapezoid. After that, the focus changes. We examine the case when ABC is a Pythagorean triangle, and find the precise conditions under which the triangle O1OO2 is also Pythagorean. A numerical table of values is also offered at the end of the paper.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
