The bisector AM of triangle ABC is perpendicular at its median BK. Find AC if AB = 1cm.
| March 8, 2021 | education
The bisector AM of triangle ABC is also the bisector of triangle ABK, and since, by condition, AM is perpendicular to ВK, then AO is not only the bisector of triangle ABC, but also its height, which is possible if triangle ABK is isosceles. Then AK = AB = 1 cm.
Since ВK is the median of the triangle ABC, then СK = AK = 1 cm, then AС = СK + AK = 1 + 1 = 2 cm.
Answer: The length of the speaker side is 2 cm.
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