The center of the triangle is circumscribed by a circle. ?
Inner heart: the intersection of bisectors of three angles of a triangle.
The center of a triangle inscribed with a circle. ?
Vertical center: the intersection of three heights of a triangle. ?
Center of gravity: the intersection of three sides of a triangle. (the center of gravity is biased to one side.
The distance between points is equal to one third of the center line of this side. )
Center: Only regular triangles (equilateral triangles) have centers.
At this time, the center of gravity, inner heart, outer heart and heart are integrated. ?
As shown in the figure:
∵? G is the center of gravity of the triangle ABC, BD=CD, AE=CE,
And AD⊥BE, BC=a, AC=b,
∴? BD=CD=a/2？ ，AE=CE=b/2？ ,
DG=AG/2？ ，EG=BG/2？ ,
AG & ampsup2+EG & amp； sup2AE & ampsup2，BG & ampsup2+DG & amp； sup2= BD & ampsup2？ ,
∴? AG & ampsup2+EG & amp； sup2+BG & amp； sup2+DG & amp； sup2AE & ampsup2+BD & amp； sup2？ ,
∴ag&； sup2+(BG/2)& amp； sup2+BG & amp； Sup2+(AG/2) and Ampsup2 = (B/2)&; sup2+(a/2)& amp； sup2？
∴? AG & ampsup2+BG & amp； sup2=(a & amp； sup2+b & amp； sup2)/5? ,
Again? AG & ampsup2+BG & amp； sup2AB & ampsup2
∴? AB & ampsup2=(a & amp； sup2+b & amp； sup2)/5? ,
∴? AB =√[5(a & amp； sup2+b & amp； sup2)]/5? ,
Or? AB =√(5a & amp； sup2+5b & amp； sup2)/5? .