The figure below shows some steps performed to circumscribe a circle about triangle ABC using only a compass and straightedge.

Which statement about segment PQ must be true?

The length of the segment is the radius of the circumscribed circle.

It meets side AB of the triangle at a right angle.

It bisects side AC of the triangle.

The distance from the midpoint of the segment to any vertex is the radius of the circumscribed circle.

Question

The figure below shows some steps performed to circumscribe a circle about triangle ABC using only a compass and straightedge. 

 

Which statement about segment PQ must be true?

 The length of the segment is the radius of the circumscribed circle.

 It meets side AB of the triangle at a right angle.

 It bisects side AC of the triangle.

 The distance from the midpoint of the segment to any vertex is the radius of the circumscribed circle.

anonymous · Answer

attachment

anonymous · Answer

the first one i think im not sure

anonymous · Answer

It isn't the first one actually. The length of PQ when drawn as a circle would be the diameter, not the radius. 

Working down the list, whether or not it is a right angle on line AB is not for sure. It LOOKS like a right angle, but unless there were more information, it is just a guess. 

In order for the third to be true, PQ would have to bisect the line AC in two even parts. You can tell just by looking at it that side A is much larger than side C when divided by line PQ. 

This leaves the last. Think carefully here as a circumscribed circle made with a compass would have to touch points A, B, and C. Meaning that the center point O to any such point would have to be the radius of the circle. Since any circle can't have more than one radius (or else it would be an oval), then that means that this statement MUST be true.

anonymous · Answer

can you help me with one more question please

anonymous · Answer

sure, link it.