自招暑期班的某几何题

chyanog

@mathematica 设S△ABC, S△AFZ, S△BDX, S△CEY, S△XYZ分别为s, s1, s2, s3, s4, 它们满足下面的方程，可以带入数值检验

1. s^9 s1^2 s2^2 s3^2-s^8 s1^2 s2^2 s3^2 (2 s1+2 s2+2 s3+9 s4)+s^7 s1 s2 s3 (-2 s1^2 s2^3+s1^3 s2 s3-6 s1^2 s2^2 s3+s1 s2^3 s3-2 s1^3 s3^2-6 s1^2 s2 s3^2-6 s1 s2^2 s3^2+s1 s2 s3^3-2 s2^2 s3^3+s1^2 s2 s3 s4+s1 s2^2 s3 s4+s1 s2 s3^2 s4+36 s1 s2 s3 s4^2)+2 s^6 s1 s2 s3 (s1^3 s2^3+s1^2 s2^4+3 s1^3 s2^2 s3+2 s1^2 s2^3 s3+s1^4 s3^2+2 s1^3 s2 s3^2+7 s1^2 s2^2 s3^2+3 s1 s2^3 s3^2+s1^3 s3^3+3 s1^2 s2 s3^3+2 s1 s2^2 s3^3+s2^3 s3^3+s2^2 s3^4-s1^2 s2^3 s4-s1^3 s2 s3 s4-14 s1^2 s2^2 s3 s4-s1 s2^3 s3 s4-s1^3 s3^2 s4-14 s1^2 s2 s3^2 s4-14 s1 s2^2 s3^2 s4-s1 s2 s3^3 s4-s2^2 s3^3 s4+20 s1^2 s2 s3 s4^2+20 s1 s2^2 s3 s4^2+20 s1 s2 s3^2 s4^2-42 s1 s2 s3 s4^3)+s^5 (s1^4 s2^6+8 s1^4 s2^5 s3+4 s1^5 s2^3 s3^2+32 s1^4 s2^4 s3^2+14 s1^3 s2^5 s3^2+14 s1^5 s2^2 s3^3+46 s1^4 s2^3 s3^3+46 s1^3 s2^4 s3^3+4 s1^2 s2^5 s3^3+s1^6 s3^4+8 s1^5 s2 s3^4+32 s1^4 s2^2 s3^4+46 s1^3 s2^3 s3^4+32 s1^2 s2^4 s3^4+4 s1^3 s2^2 s3^5+14 s1^2 s2^3 s3^5+8 s1 s2^4 s3^5+s2^4 s3^6-s1^3 s2^6 s4-19 s1^4 s2^4 s3 s4-8 s1^3 s2^5 s3 s4-2 s1^5 s2^2 s3^2 s4-62 s1^4 s2^3 s3^2 s4-119 s1^3 s2^4 s3^2 s4-2 s1^2 s2^5 s3^2 s4-s1^6 s3^3 s4-8 s1^5 s2 s3^3 s4-119 s1^4 s2^2 s3^3 s4-216 s1^3 s2^3 s3^3 s4-62 s1^2 s2^4 s3^3 s4-19 s1^4 s2 s3^4 s4-62 s1^3 s2^2 s3^4 s4-119 s1^2 s2^3 s3^4 s4-19 s1 s2^4 s3^4 s4-2 s1^2 s2^2 s3^5 s4-8 s1 s2^3 s3^5 s4-s2^3 s3^6 s4+19 s1^3 s2^4 s3 s4^2+43 s1^4 s2^2 s3^2 s4^2+223 s1^3 s2^3 s3^2 s4^2+43 s1^2 s2^4 s3^2 s4^2+19 s1^4 s2 s3^3 s4^2+223 s1^3 s2^2 s3^3 s4^2+223 s1^2 s2^3 s3^3 s4^2+43 s1^2 s2^2 s3^4 s4^2+19 s1 s2^3 s3^4 s4^2-149 s1^3 s2^2 s3^2 s4^3-149 s1^2 s2^3 s3^2 s4^3-149 s1^2 s2^2 s3^3 s4^3+126 s1^2 s2^2 s3^2 s4^4)+s^4 s1 s2 s3 (2 s1^4 s2^4+6 s1^3 s2^5+14 s1^4 s2^3 s3+34 s1^3 s2^4 s3+2 s1^2 s2^5 s3+2 s1^5 s2 s3^2+42 s1^4 s2^2 s3^2+82 s1^3 s2^3 s3^2+42 s1^2 s2^4 s3^2+6 s1^5 s3^3+34 s1^4 s2 s3^3+82 s1^3 s2^2 s3^3+82 s1^2 s2^3 s3^3+14 s1 s2^4 s3^3+2 s1^4 s3^4+14 s1^3 s2 s3^4+42 s1^2 s2^2 s3^4+34 s1 s2^3 s3^4+2 s2^4 s3^4+2 s1 s2^2 s3^5+6 s2^3 s3^5-2 s1^4 s2^3 s4-32 s1^3 s2^4 s4-6 s1^2 s2^5 s4-2 s1^5 s2 s3 s4-48 s1^4 s2^2 s3 s4-166 s1^3 s2^3 s3 s4-82 s1^2 s2^4 s3 s4-2 s1 s2^5 s3 s4-6 s1^5 s3^2 s4-82 s1^4 s2 s3^2 s4-352 s1^3 s2^2 s3^2 s4-352 s1^2 s2^3 s3^2 s4-48 s1 s2^4 s3^2 s4-32 s1^4 s3^3 s4-166 s1^3 s2 s3^3 s4-352 s1^2 s2^2 s3^3 s4-166 s1 s2^3 s3^3 s4-2 s2^4 s3^3 s4-2 s1^3 s3^4 s4-48 s1^2 s2 s3^4 s4-82 s1 s2^2 s3^4 s4-32 s2^3 s3^4 s4-2 s1 s2 s3^5 s4-6 s2^2 s3^5 s4+27 s1^3 s2^3 s4^2+30 s1^2 s2^4 s4^2+36 s1^4 s2 s3 s4^2+299 s1^3 s2^2 s3 s4^2+340 s1^2 s2^3 s3 s4^2+36 s1 s2^4 s3 s4^2+30 s1^4 s3^2 s4^2+340 s1^3 s2 s3^2 s4^2+804 s1^2 s2^2 s3^2 s4^2+299 s1 s2^3 s3^2 s4^2+27 s1^3 s3^3 s4^2+299 s1^2 s2 s3^3 s4^2+340 s1 s2^2 s3^3 s4^2+27 s2^3 s3^3 s4^2+36 s1 s2 s3^4 s4^2+30 s2^2 s3^4 s4^2-25 s1^2 s2^3 s4^3-160 s1^3 s2 s3 s4^3-515 s1^2 s2^2 s3 s4^3-160 s1 s2^3 s3 s4^3-25 s1^3 s3^2 s4^3-515 s1^2 s2 s3^2 s4^3-515 s1 s2^2 s3^2 s4^3-160 s1 s2 s3^3 s4^3-25 s2^2 s3^3 s4^3+250 s1^2 s2 s3 s4^4+250 s1 s2^2 s3 s4^4+250 s1 s2 s3^2 s4^4-126 s1 s2 s3 s4^5)+s^3 s1 s2 s3 (s1^5 s2^3 s3+10 s1^4 s2^4 s3+13 s1^3 s2^5 s3+6 s1^5 s2^2 s3^2+44 s1^4 s2^3 s3^2+52 s1^3 s2^4 s3^2+6 s1^2 s2^5 s3^2+13 s1^5 s2 s3^3+52 s1^4 s2^2 s3^3+91 s1^3 s2^3 s3^3+44 s1^2 s2^4 s3^3+s1 s2^5 s3^3+10 s1^4 s2 s3^4+44 s1^3 s2^2 s3^4+52 s1^2 s2^3 s3^4+10 s1 s2^4 s3^4+s1^3 s2 s3^5+6 s1^2 s2^2 s3^5+13 s1 s2^3 s3^5-s1^5 s2^3 s4-2 s1^4 s2^4 s4-6 s1^3 s2^5 s4-6 s1^5 s2^2 s3 s4-68 s1^4 s2^3 s3 s4-107 s1^3 s2^4 s3 s4-29 s1^2 s2^5 s3 s4-29 s1^5 s2 s3^2 s4-178 s1^4 s2^2 s3^2 s4-376 s1^3 s2^3 s3^2 s4-178 s1^2 s2^4 s3^2 s4-6 s1 s2^5 s3^2 s4-6 s1^5 s3^3 s4-107 s1^4 s2 s3^3 s4-376 s1^3 s2^2 s3^3 s4-376 s1^2 s2^3 s3^3 s4-68 s1 s2^4 s3^3 s4-s2^5 s3^3 s4-2 s1^4 s3^4 s4-68 s1^3 s2 s3^4 s4-178 s1^2 s2^2 s3^4 s4-107 s1 s2^3 s3^4 s4-2 s2^4 s3^4 s4-s1^3 s3^5 s4-6 s1^2 s2 s3^5 s4-29 s1 s2^2 s3^5 s4-6 s2^3 s3^5 s4+4 s1^4 s2^3 s4^2+19 s1^3 s2^4 s4^2+6 s1^2 s2^5 s4^2+16 s1^5 s2 s3 s4^2+136 s1^4 s2^2 s3 s4^2+356 s1^3 s2^3 s3 s4^2+199 s1^2 s2^4 s3 s4^2+16 s1 s2^5 s3 s4^2+6 s1^5 s3^2 s4^2+199 s1^4 s2 s3^2 s4^2+794 s1^3 s2^2 s3^2 s4^2+794 s1^2 s2^3 s3^2 s4^2+136 s1 s2^4 s3^2 s4^2+19 s1^4 s3^3 s4^2+356 s1^3 s2 s3^3 s4^2+794 s1^2 s2^2 s3^3 s4^2+356 s1 s2^3 s3^3 s4^2+4 s2^4 s3^3 s4^2+4 s1^3 s3^4 s4^2+136 s1^2 s2 s3^4 s4^2+199 s1 s2^2 s3^4 s4^2+19 s2^3 s3^4 s4^2+16 s1 s2 s3^5 s4^2+6 s2^2 s3^5 s4^2-14 s1^3 s2^3 s4^3-17 s1^2 s2^4 s4^3-100 s1^4 s2 s3 s4^3-486 s1^3 s2^2 s3 s4^3-526 s1^2 s2^3 s3 s4^3-100 s1 s2^4 s3 s4^3-17 s1^4 s3^2 s4^3-526 s1^3 s2 s3^2 s4^3-1201 s1^2 s2^2 s3^2 s4^3-486 s1 s2^3 s3^2 s4^3-14 s1^3 s3^3 s4^3-486 s1^2 s2 s3^3 s4^3-526 s1 s2^2 s3^3 s4^3-14 s2^3 s3^3 s4^3-100 s1 s2 s3^4 s4^3-17 s2^2 s3^4 s4^3+11 s1^2 s2^3 s4^4+233 s1^3 s2 s3 s4^4+591 s1^2 s2^2 s3 s4^4+233 s1 s2^3 s3 s4^4+11 s1^3 s3^2 s4^4+591 s1^2 s2 s3^2 s4^4+591 s1 s2^2 s3^2 s4^4+233 s1 s2 s3^3 s4^4+11 s2^2 s3^3 s4^4-233 s1^2 s2 s3 s4^5-233 s1 s2^2 s3 s4^5-233 s1 s2 s3^2 s4^5+84 s1 s2 s3 s4^6)+s^2 s1 s2 s3 (4 s1^5 s2^3 s3^2+16 s1^4 s2^4 s3^2+12 s1^3 s2^5 s3^2+12 s1^5 s2^2 s3^3+36 s1^4 s2^3 s3^3+36 s1^3 s2^4 s3^3+4 s1^2 s2^5 s3^3+16 s1^4 s2^2 s3^4+36 s1^3 s2^3 s3^4+16 s1^2 s2^4 s3^4+4 s1^3 s2^2 s3^5+12 s1^2 s2^3 s3^5-4 s1^5 s2^3 s3 s4-18 s1^4 s2^4 s3 s4-15 s1^3 s2^5 s3 s4-34 s1^5 s2^2 s3^2 s4-124 s1^4 s2^3 s3^2 s4-142 s1^3 s2^4 s3^2 s4-34 s1^2 s2^5 s3^2 s4-15 s1^5 s2 s3^3 s4-142 s1^4 s2^2 s3^3 s4-261 s1^3 s2^3 s3^3 s4-124 s1^2 s2^4 s3^3 s4-4 s1 s2^5 s3^3 s4-18 s1^4 s2 s3^4 s4-124 s1^3 s2^2 s3^4 s4-142 s1^2 s2^3 s3^4 s4-18 s1 s2^4 s3^4 s4-4 s1^3 s2 s3^5 s4-34 s1^2 s2^2 s3^5 s4-15 s1 s2^3 s3^5 s4+s1^3 s2^5 s4^2+22 s1^5 s2^2 s3 s4^2+92 s1^4 s2^3 s3 s4^2+116 s1^3 s2^4 s3 s4^2+35 s1^2 s2^5 s3 s4^2+35 s1^5 s2 s3^2 s4^2+286 s1^4 s2^2 s3^2 s4^2+540 s1^3 s2^3 s3^2 s4^2+286 s1^2 s2^4 s3^2 s4^2+22 s1 s2^5 s3^2 s4^2+s1^5 s3^3 s4^2+116 s1^4 s2 s3^3 s4^2+540 s1^3 s2^2 s3^3 s4^2+540 s1^2 s2^3 s3^3 s4^2+92 s1 s2^4 s3^3 s4^2+92 s1^3 s2 s3^4 s4^2+286 s1^2 s2^2 s3^4 s4^2+116 s1 s2^3 s3^4 s4^2+22 s1^2 s2 s3^5 s4^2+35 s1 s2^2 s3^5 s4^2+s2^3 s3^5 s4^2-2 s1^3 s2^4 s4^3-s1^2 s2^5 s4^3-20 s1^5 s2 s3 s4^3-162 s1^4 s2^2 s3 s4^3-326 s1^3 s2^3 s3 s4^3-190 s1^2 s2^4 s3 s4^3-20 s1 s2^5 s3 s4^3-s1^5 s3^2 s4^3-190 s1^4 s2 s3^2 s4^3-799 s1^3 s2^2 s3^2 s4^3-799 s1^2 s2^3 s3^2 s4^3-162 s1 s2^4 s3^2 s4^3-2 s1^4 s3^3 s4^3-326 s1^3 s2 s3^3 s4^3-799 s1^2 s2^2 s3^3 s4^3-326 s1 s2^3 s3^3 s4^3-162 s1^2 s2 s3^4 s4^3-190 s1 s2^2 s3^4 s4^3-2 s2^3 s3^4 s4^3-20 s1 s2 s3^5 s4^3-s2^2 s3^5 s4^3+s1^3 s2^3 s4^4+2 s1^2 s2^4 s4^4+92 s1^4 s2 s3 s4^4+383 s1^3 s2^2 s3 s4^4+398 s1^2 s2^3 s3 s4^4+92 s1 s2^4 s3 s4^4+2 s1^4 s3^2 s4^4+398 s1^3 s2 s3^2 s4^4+912 s1^2 s2^2 s3^2 s4^4+383 s1 s2^3 s3^2 s4^4+s1^3 s3^3 s4^4+383 s1^2 s2 s3^3 s4^4+398 s1 s2^2 s3^3 s4^4+s2^3 s3^3 s4^4+92 s1 s2 s3^4 s4^4+2 s2^2 s3^4 s4^4-s1^2 s2^3 s4^5-160 s1^3 s2 s3 s4^5-367 s1^2 s2^2 s3 s4^5-160 s1 s2^3 s3 s4^5-s1^3 s3^2 s4^5-367 s1^2 s2 s3^2 s4^5-367 s1 s2^2 s3^2 s4^5-160 s1 s2 s3^3 s4^5-s2^2 s3^3 s4^5+124 s1^2 s2 s3 s4^6+124 s1 s2^2 s3 s4^6+124 s1 s2 s3^2 s4^6-36 s1 s2 s3 s4^7)+s s1^2 s2^2 s3^2 (s1-s4) (s2-s4) (s3-s4) (s1+s2+s3-s4) (4 s1^2 s2 s3+4 s1 s2^2 s3+4 s1 s2 s3^2-5 s1^2 s2 s4-7 s1 s2^2 s4-7 s1^2 s3 s4-21 s1 s2 s3 s4-5 s2^2 s3 s4-5 s1 s3^2 s4-7 s2 s3^2 s4+8 s1^2 s4^2+21 s1 s2 s4^2+8 s2^2 s4^2+21 s1 s3 s4^2+21 s2 s3 s4^2+8 s3^2 s4^2-17 s1 s4^3-17 s2 s4^3-17 s3 s4^3+9 s4^4)-s1^2 s2^2 s3^2 (s1-s4)^2 (s2-s4)^2 (s3-s4)^2 (s1+s2+s3-s4)^2 s4=0

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