The bisector AL of triangle ABC divides side BC in a 2: 1 ratio. In what respect does the median CM divide this bisector.
| March 1, 2021 | education
Let the length of the segment CB = X cm, then the length of the segment CL = 2 * X cm.
Through the vertex A of triangle ABC, draw a segment AK until the intersection of the continuation of the median CM.
The formed triangle AMK is equal to the CBM triangle along the side and two corners. Then AK = СВ = 2 * X + X = 3 * X cm.
Triangles AOK and СOL are similar in two angles, then AK / OA = CL / OL.
3 * X / OK = 2 * X / OL.
OL / OK = 2/3.
Answer: the median divides the bisector in the ratio of 2/3.
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