Straight lines OA, OB, OC are pairwise perpendicular. Find the length of the segment AB if OC = 10 cm

Straight lines OA, OB, OC are pairwise perpendicular. Find the length of the segment AB if OC = 10 cm, AC = 5√5 cm, BC = 2 √61 cm.

Consider a right-angled triangle ВСО, in which we find a leg ОВ according to the Pythagorean theorem.
ОВ ^ 2 = ВС ^ 2 – ОС ^ 2 = (2 * √61) ^ 2 – (10) ^ 2 = 4 * 61 + 100 = 144.
Consider a right-angled triangle ASO, in which we find the leg OA according to the Pythagorean theorem.
OA ^ 2 = AC ^ 2 – OC ^ 2 = (5 * √5) ^ 2 – (10) ^ 2 = 25 * 5 – 100 = 25.
Consider a right-angled triangle ABO, in which we find the hypotenuse AB by the Pythagorean theorem.
AB ^ 2 = OB ^ 2 + OB ^ 2 = 144 + 25 = 169.
AB = 13.
Answer: The length of the segment AB = 13 cm.