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一个三角形,除了三个内角A、B、C及其外角外,它的元素还有三条边a、b、c,三条高h_a、h_b、h_c,三条中线m_a、m_b、m_c,三条内角平分线t_a、t_b,t_c,三条外角平分线t_a’、t_b’、t_c’,以及周长2p,面积S,外接圆半径R,内切圆半径r,旁切圆半径r_a、r_b、r_c等(其中a为A所对的边,h_a为a边上的高,其它类推)。我们在编制三角形的计算题时,为了避免具体计算的繁冗,往往希望把线段的长或者面积的值凑成整数。这样,不但便于计算与说明,而且还可以给人一种数学美的享受。试想,利用勾股定理,当
A triangle has three edges a, b, c, three heights h_a, h_b, h_c, three midlines m_a, m_b, m_c, and three internal angle bisectors, in addition to the three interior angles A, B, C and their outer corners. T_a, t_b, t_c, three outer angle bisectors t_a’, t_b’, t_c’, and perimeter 2p, area S, circumcircle radius R, radius of inscribed circle r, radius of sidecut circle r_a, r_b, r_c, etc. ( A is the edge of A, h_a is the height of edge a, and so on.) When we formulate the triangle calculation problem, in order to avoid the tedious calculation, we often want to make the value of the length or area of the segment into an integer. In this way, not only is it easy to calculate and explain, but it can also give people a mathematical beauty. Imagine using the Pythagorean theorem when