In an isosceles triangle ABC (BC-base), the medians intersect at point O. Find OB if AB = AC = 13cm, BC = 10cm.
| September 25, 2021 | education
The median AH, which is also the height of the triangle in an isosceles triangle, divides the base of the BC in half.
СН = ВН = ВС / 2 = 10/2 = 5 cm.
In a right-angled triangle ACH, we determine the length of the leg AH.
AH ^ 2 = AC ^ 2 – CH ^ 2 = 169 – 25 = 144.
AH = 12 cm.
The medians of the triangle of the intersection point are divided in the ratio of 2/1, then AO = 2 * OH.
3 * OH = AH = 12 cm.
OH = 12/3 = 4 cm.
From the right-angled triangle BOH, we define the hypotenuse BO.
BO ^ 2 = OH ^ 2 + BH ^ 2 = 16 + 25 = 41.
BO = √41 cm.
Answer: The length of the VO segment is √41 cm.
One of the components of a person's success in our time is receiving modern high-quality education, mastering the knowledge, skills and abilities necessary for life in society. A person today needs to study almost all his life, mastering everything new and new, acquiring the necessary professional qualities.
