The point is removed from the oblique of the vertices of the right-angled triangle at a distance of 10 cm.

The point is removed from the oblique of the vertices of the right-angled triangle at a distance of 10 cm. At what distance from the plane of the triangle is this point, if the median drawn to the hypotenuse is 5 cm?

Let’s connect point D with the vertices of the triangle ABC.

In the learned pyramid DABС, the lateral edges are equal, then point D is projected to the center of the circle circumscribed about the triangle, point H. The center of the circumscribed circle near the right-angled triangle is the midpoint of its hypotenuse.

The CDH triangle is rectangular, then DH: 2 = CD: 2 – CH: 2 = 100 – 25 = 75.

DН = 5 * √3 cm.

Answer: The point is removed at a distance of 5 * √3 cm.