In △abc, cm is the median to ab and side bc is 12 cm long. there is a point p∈ cm and a line ap intersecting bc at point q. find the lengths of segments cq and bq , if p is the midpoint of cm

CQ=4 cm, BQ=8 cm

Step-by-step explanation:

In given triangle ABC draw the line MD parallel to the AQ.

1. Consider triangle AMD. In this triangle PQ║MD (build) and CP=PM (P is midpoint of CM). Then by the triangle midline theorem,  line PQ is midline of triangle AMD and CQ=QD.

2. Consider triangle BAQ. In this triangle AQ║MD and AM=MB. Then by the triangle midline theorem,  line MD is midline of triangle BAQ and BD=QD.

Hence, CQ=QD=BD. Since BC=12 cm and

BC=BQ+QD+BD,

then  

Note that

BQ=BD+QD=4+4=8 cm.

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6 meters

step-by-step explanation: