3. Point Ris the centroid of Delta ABC,AR=8,RC=12,BD=10 and BE=15. Find each indicated measure. The point of con concurrency of the 3 medians is called the square A median is a segment that conny vertex to the square of the opposite side. possible answers for statement above: (centroid circumcenter, incenter, orthocenter , midpoint, side, vertex, ongle) DR= BC= BR=

The question provides that point R is the centroid of triangle ABC which divides the medians into the ratios of 2:1. It also mentions some measure for two more line segments BD and BE. It finally asks for specific measures in triangle like segment DR, BC and BR.a) In a triangle, the properties of the centroid is such that it divides the median (he line from a vertex to the midpoint of the opposite side) in a ratio of 2:1. Here since and , these already are in the ratio 2:1 implying 'R' is two thirds the distance from vertex 'A' to the midpoint of BC. b) The point of concurrency (point where they intersect) for medians in a triangle is called centroid. In here, for completion of the given statement in the problem, we will select the empty squares to be "centroid" and "midpoint". A median is a segment that connects a vertex to the "midpoint" of the opposite side. c) - Since BD is given as 10 units and DR is one third of BD (property of centroid), so, d) - Since BE is marked as 15units, which is two thirds of the length (lines are in ratio 2:1), hence e) - Now BR = BD - DR = 10 - 10/3 = 20/3 Using the principles and properties of centroids, and magnitudes, we have these values.