Question

设直角三角形的两条直角边长及斜边上的高分别为a，b，h。求证1/a^2+1/b^2=1/h^2

Answer 1

假设斜边是C
则a^2+b^2=c^2
ab=ch
1/a^2+1/b^2
=(a^2+b^2)/a^2b^2
=(a^2+b^2)/(ab)^2
=c^2/(ch)^2
=c^2/c^2h^2
=1/h^2