Question

Frank is constructing the circumscribed circle for △XYZ. He has already used his compass and straightedge to complete the part of the construction shown in the figure.

Which construction could be his next step?


Place the point of the compass on point Y and draw an arc intersecting the two arcs.

Place the point of the compass on point X and draw an arc intersecting the two arcs.

Place the point of the compass on point Z and draw an arc through points X and Y.

Place the point of the compass on one of the arcs and draw an arc through point X.

Answer 1

Place the point of the compass on point X and draw an arc intersecting the two arcs.

Step-by step explanation:

This is to complete the angle bisector.

Answer 2

circumscribed circle for a triangle is circle where the circumference would cut all the vertices in the triangle
the diagram already has arcs marked from point Y, with the aim of drawing a perpendicular bisector to line XY.

Therefore the next step is to place the compass on point X and draw two arcs which cross the arcs already drawn (second option is the correct answer)

The points at which the 2 arcs meet are connected to each other making a perpendicular bisector that would cut XY perpendicularly.

Next step is to place the compass at Z and draw 2 arcs between Z and Y points, similarly place the compass at Y and draw 2 arcs that would cut the arcs already drawn.

Then connect the two points where the arcs meet and thats the perpendicular bisector of ZY.
The point at which perpendicular bisectors of XY and YZ meet is known as the circumcenter. Place the compass on this point with the radius any of the three points X,Y or Z and draw the circle