- AIt is similar to triangle ABC, and each of its sides is half of the corresponding side of ABC
- BIt has the same centroid as triangle ABC
- CIts circumcentre is the same point as the circumcentre of triangle ABC
- DIt cuts triangle ABC into four triangles that are all congruent to one another
Step-by-Step Solution
The mid-point theorem makes every side of the medial triangle parallel to a side of ABC and half its length, so the two triangles are similar in the ratio 1 : 2 and the four small triangles are congruent. The medians of ABC are also the medians of the medial triangle, so the centroid is shared. But the circumcircle of the medial triangle is precisely the NINE-POINT circle, centred at the midpoint of OH — not at O. In fact the perpendicular bisectors of ABC are the altitudes of the medial triangle, so O is its ORTHOCENTRE. The two centres coincide only when the triangle is equilateral and every centre collapses to one point.
Answer: C) Its circumcentre is the same point as the circumcentre of triangle ABC