A ball with a radius of 11 touches two mutually perpendicular planes. Find the distance from the center
| August 22, 2021 | education
A ball with a radius of 11 touches two mutually perpendicular planes. Find the distance from the center of the ball to the line of intersection of these planes.
If the ball touches the plane, then the distance from the center of the ball to the plane is equal to the radius of the ball.
AM = BM = R = 11.
The angle AOB is equal to 90º, since, according to the condition of the problem, the intersecting areas are perpendicular.
We have: two adjacent sides of the quadrilateral are equal, the angle between them is straight.
So the figure AOBM is a square
Find the diagonal of the square OM:
ОМ² = 2 * 11².
OM = √2 * 11 = 15.56.
Answer: the distance from the center of the ball to the line of intersection of the planes √2 * 11
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