In triangle ABC, point N is the midpoint of the median AM. Line CN intersects AB at point P. Find AP: BP.
| March 20, 2021 | education
Through point M we construct a segment DM parallel to AC and DM = AC.
Quadrangle АСМD parallelogram, then АD = ВМ and АD || ВM. Then the quadrilateral ADBM is also a parallelogram. Let’s mark the point K, the intersection of AB and DM. AK = ВK as halves of the parallelogram diagonals.
In the triangle ADM, AK and DH its median, then by the property of the median, AР = 2 * РK.
AK = ВK = 3 * RK.
Then BP = ВK + РK = 4 * РK.
AР / BP = 2 * РK / 4 * RK = 1/2.
Answer: Line segments are referred to as 1/2.
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