Question

ZE is the angle bisector of measure YEX and the perpendicular bisector of GF, GX is the angle bisector of measure YGZ and the perpendicular bisector of EF, FY is the angle bisector of measure ZFX and the perpendicular bisector of EG. Point A is the intersection of EZ, GX, and FY.

Answer 1

C

Explanation:

The center of inscribed circle into triangle is point of intersection of all interior angles of triangle.

The center of circumscribed circle over triabgle is point of intersection of perpendicular bisectors to the sides.

Circumscribed circle always passes through the vertices of the triangle.

Inscribed circle is always tangent to the triangle's sides.

In your case angles' bisectors and perpendicular bisectors intesect at one point, so point A is the center of inscribed circle and the center of corcumsribed circle. Thus, these circles pass through the points X, Y, Z and G, E, F, respectively.