In the triangle ABC, the median AA1 BB1 CC1 equal to 6 cm, 9 cm, 12 cm, respectively, intersect

In the triangle ABC, the median AA1 BB1 CC1 equal to 6 cm, 9 cm, 12 cm, respectively, intersect at point O. Find AO + OB + CO

By the property of the bisectors of a triangle, the point of their intersection, point O, divides the bisectors in a ratio of 2/1 starting from the apex of the triangle.

OA / OA1 = 2/1.

OA1 = OA / 2.

AA1 = OA + OA1 = AO + AO / 2 = 3 * AO / 2.

AO = 2 * AA1 / 3 = 2 * 6/3 = 4 cm.

Similarly, OB = 2 * BB1 / 3 = 2 * 9/3 = 6 cm, OC = 2 * CC1 / 3 = 2 * 12/3 = 8 cm.

Then OA + OB + OS = 4 + 6 + 8 = 18 cm.

Answer: The sum of the segments is 18 cm.