Question

below are the steps for constructing the circumscribed circle of a triangle using a compass and straightedge. which answer choice has the steps in the correct or - circle ( p ) is circumscribed about ( \triangle xyz ). - place the compass point at ( p ) and adjust the setting so that the pencil is - given ( \triangle xyz ), construct the perpendicular bisectors of ( overline{xy} ) and ( overline{yz} ). - without changing the compass setting, draw the circle with center ( p ) an ( overline{xp} ). - label the circumcenter ( p ). ( \bigcirc ) 3, 2, 5, 4, 1 ( \bigcirc ) 3, 5, 4, 2, 1 ( \bigcirc ) 3, 5, 2, 4, 1 ( \bigcirc ) 1, 3, 5, 2, 4

Explanation:

Step1: Identify the starting step

The construction starts with the given triangle, so the first step is "Given $\triangle XYZ$, construct the perpendicular bisectors of $\overline{XY}$ and $\overline{YZ}$" (step 3).

Step2: Find the circumcenter

Next, we label the intersection of the perpendicular bisectors as the circumcenter $P$, so the second step is "Label the circumcenter $P$" (step 5).

Step3: Set the compass

Then, we place the compass at $P$ and set it to the length of $XP$ (or any vertex to $P$), so the third step is "Place the compass point at $P$ and adjust the setting so that the pencil is at $X$ (or the length of $\overline{XP}$)" (step 2). Wait, actually, the step is "Place the compass point at $P$ and adjust the setting so that the pencil is at $X$ (to get the radius $XP$)".

Step4: Draw the circle

After setting the compass, we draw the circle with center $P$ and radius $XP$ (or the set length), so the fourth step is "Without changing the compass setting, draw the circle with center $P$ and radius $XP$" (step 4).

Step5: State the result

Finally, we have the circle circumscribed about the triangle, so the fifth step is "Circle $P$ is circumscribed about $\triangle XYZ$" (step 1).

Putting the steps in order: 3 (given, construct perpendicular bisectors), 5 (label circumcenter $P$), 2 (place compass at $P$ and set to $XP$), 4 (draw the circle), 1 (circle is circumscribed). So the order is 3, 5, 2, 4, 1.

Answer:

3, 5, 2, 4, 1 (corresponding to the option "3, 5, 2, 4, 1")