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LuckyWell [14K]
3 years ago
9

ZE 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.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.

Mathematics
2 answers:
frozen [14]3 years ago
6 0

Answer:

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.

Step-by-step explanation:

A is the intersection of angle bisectors, so is the incenter of triangle EFG. It is also the intersection of the perpendicular bisectors of the sides of triangle EFG, so is the circumcenter.

The altitudes at X, Y, and Z are perpendicular to sides EF, EG, and FG, and pass through the incenter, so X, Y, Z are points on the incircle.

A is the center of circles through E, F, and G, and through X, Y, and Z.

OverLord2011 [107]3 years ago
6 0

Answer:

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.

C on edg2020

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Step-by-step explanation:

<u>Concept:</u>

Here, we need to know the idea of the circle formula.

Circle formula: (x - h)² + (y - k)² = r²

Center = (h, k)

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If you are still confused, please refer to the attachment below for a graphical explanation.

<u>Solve:</u>

Center = (2, 14)

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<em>Given formula</em>

(x - h)² + (y - k)² = r²

<em>Substitute the value into the formula</em>

(x - 2)² + (y - 14)² = (1)²

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