Lines AB and CD are perpendicular to a certain plane and intersect it at points B

Lines AB and CD are perpendicular to a certain plane and intersect it at points B and D, respectively. Find AC if AB = 9, CD = 15, BD = 8 (consider 2 cases)

1 case:

When points A and C are located on the same side of the plane. In this case, you don’t even need to count anything. If two straight lines are perpendicular to the plane, then they are parallel (property). Hence, according to Thales’ theorem, all the segments between them are equal. AC = BD = 8.

2 case:

If A and C are on opposite sides of the plane. To begin with, draw a perpendicular AH to the straight line CD. It will be equal to 8 (by Thales’ theorem). HD = AB (also by Thales’ theorem, AH = BD) = 9.

By the Pythagorean theorem: AC = √ (8 * 8 + 24 * 24) = √640 = 8√10