In problem 4, you will be given a triangle. Use your compass and straightedge to draw in the perpendicular bisectors of the three sides, the bisectors of the three angles, the three medians, and the three altitudes. To draw a median, connect a vertex of the triangle with the midpoint of the opposite side, You will already have the midpoint of the three sides as a result of having already constructed the perpendicular bisectors of the three sides. To draw an altitude, from a vertex of the triangle, drop a perpendicular to the opposite side. You should find that the three perpendicular bisectors meet at a single point which is the center of the circumscribed circle. Draw the circle centered at this point that goes through all three vertices of the triangle. You should also find that the three angle bisectors all meet at the same point, This point is the center of the inscribed triangle. To draw the inscribed triangle, now that you have its center, you need a point on the circle. To find one, drop a perpendicular from the point where the three angle bisectors meet to one of the sides. The point where the perpendicular meets the side will be the point of tangency for that side which will be a point on the circle. Similarly, the three medians will meet at a single point, which is called the centroid, and the three altitudes will meet at a single point which is called the orthocenter. The Euler line goes through the orthocenter, the centroid, and the center of the circumscribed circle.