Question

已知球面上三点A.B、C,AB=3,BC=4,AC=5,球半径为6.5,求球心O到平面ABC的距离

Answer 1

设三角形ABC的外接圆半径为r,球半径为R,球心O到平面ABC的距离h

因为AB^2+BC^2=3^2+4^2=5^2=AC^2

所以ABC是直角三角形

则r=AC/2=2.5

因R^2=h^2+r^2

h^2=R^2-r^2=6.5^2-2.5^2=36

解得h=6