Question

Line segment Z E is the angle bisector of AngleYEX and the perpendicular bisector of Line segment G F. Line segment G X is the angle bisector of AngleYGZ and the perpendicular bisector of Line segment E F. Line segment F Y is the angle bisector of AngleZFX and the perpendicular bisector of Line segment E G. Point A is the intersection of Line segment E Z, Line segment G X, and Line segment F Y.
Triangle G E F has angles with different measures. Point A is at the center. Lines are drawn from the points of the triangle to point A. Lines are drawn from point A to the sides of the triangle to form right angles and line segments A X, A Z, and A Y.
Which must be true?

Point A is the center of the circle that passes through points E, F, and G but is not the center of the circle that passes through points X, Y, and Z.
Point A is the center of the circle that passes through points X, Y, and Z but is not the center of the circle that passes through points E, F, and G.
Point A is the center of the circle that passes through points E, F, and G and the center of the circle that passes through points X, Y, and Z.
Point A is not necessarily the center of the circle that passes through points E, F, and G or the center of the circle that passes through points X, Y, and Z

Answer 1

The correct option that depicts the centroid of the triangle is; C. Point A is the center of the circle that passes that passes through the points E, F and G and is the center of the circle that passes through the points X, Y and Z.

How to interpret the segments formed from Triangle Centroid?

The center of inscribed circle into the triangle is the point where the angle bisectors of the triangle meet.

The center of the circumscribed circle over the triangle is the point where the perpendicular bisectors of the sides meet.

Line segments ZE, FY and GX are both angle bisectors and perpendicular bisectors of the sides. Thus, the point of intersection of line segments ZE, FY and GX is the center of inscribed circle into the triangle and the center of the circumscribed circle over the triangle.

Inscribed circle passes through the points X, Y and Z. Circumscribed circle passes through the points E, F and G. So, point A is the center of the circle that passes that passes through the points E, F and G and is the center of the circle that passes through the points X, Y and Z.

Thus, the correct option is option C. Point A is the center of the circle that passes that passes through the points E, F and G and is the center of the circle that passes through the points X, Y and Z.

Read more about Triangle Centroid at; brainly.com/question/7644338

#SPJ1