Question

josephine is constructing a circle circumscribed about triangle xyz. she uses the following sequence of steps to construct the circle.

1. she constructs the perpendicular bisectors of two sides.
2. she finds their point of intersection, p.
3. she uses a compass, with the fixed end on x, to draw a circle passing through point p.

did josephine make any errors while constructing the circle?
a. yes, she should have constructed the angle bisectors.
b. yes, she should have found the perpendicular bisectors of all 3 sides.
c. yes, she should have placed the compass with the fixed end on p and drawn a circle through point x.
d. no, she did not make any errors.

Explanation:

The point of intersection of a triangle's perpendicular bisectors (point P) is the circumcenter, which is the center of the circumscribed circle. To draw the circumscribed circle, the compass must be anchored at this center (P), with the compass width set to the distance from P to any vertex (like X) to ensure the circle passes through all three vertices of the triangle. Josephine incorrectly anchored the compass at vertex X instead of the circumcenter P.

Answer:

C. Yes, she should have placed the compass with the fixed end on P and drawn a circle through point X.