The bisector AM and the median BK of the right-angled triangle ABC (angle B = 90)
| August 20, 2021 | education
The bisector AM and the median BK of the right-angled triangle ABC (angle B = 90) intersect at the point O, AB = 8, BC = 6. Find the relationship BО: OK
We calculate the length of the hypotenuse by the Pythagorean theorem:
AC = √ (8² + 6²) = √ (64 + 36) = √100 = 10.
The median of a right-angled triangle is half the hypotenuse. BK = AK = KC = 10/2 = 5.
According to the property of the bisector of the tracker: BО / AB = OK / AK; BО / OK = AB / AK = 8/5.
Answer: the ratio BО: OK = 8: 5.
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