Question

Point Y is the circumcenter of triangle D E F. Lines are drawn from the points of the triangles to point Y. Lines are drawn from point Y to the sides of the triangle to form right angles and line segments Y L, Y M, and Y N. The line segments cut the sides of the triangles into 2 equal parts. Which statement is true about point Y?

A) Point Y is the center of the circle that passes through points D, F, and N.
B) Point Y is the center of the circle that passes through points M, N, and E.
C) Point Y is the center of the circle that passes through points L, M, and N.
D) Point Y is the center of the circle that passes through points D, E, and F.

Answer 1

Point Y is the center of the circle that passes through points D, E, and F.

Answer 2

Point Y is the center of the circle that passes through points D, E, and F.

Explanation:

If we draw a circle through all the vertices of a triangle then the circle obtained is the circumcircle of the given triangle.

And the circumcenter is the center point of the circumcircle which is obtained by the point of intersection of the perpendicular bisector of all the sides of the triangle.

Therefore, since Y is the circumcenter of the triangle DEF, so, point Y is the center of the circle that passes through points D, E, and F. (Answer)