a The center should be equidistant from the three points.
B
b To find the circumcenter of a triangle you need to use a compass.
A
a See solution.
B
b x=7, y=7
Practice makes perfect
a To find the center of a circle that passes through three known points, we can draw a triangle between the points and then proceed to find the triangle's circumcenter.
Why does this work?
This works because the circumcenter is equidistant from the triangles vertices. Since the points are also on the circle, the segments between the points and the circumcenter must also be the circle's radius.
b Let's copy the diagram. We will also go ahead and draw the circle and the triangle.
To find the circumcenter, we have to graph the perpendicular bisectors of at least two of the triangle's sides.
We will start by finding the perpendicular bisector to BC. We draw two circles, one around B and one around C using a compass. Make sure the compass setting is the same for both circles and that the radius is greater than half the length of BC.
The perpendicular bisector is the segment where the two circles intersect.
Let's repeat the procedure for AC. Notice that the circle we drew around C covers half the length of AC so by keeping that compass setting intact we can make a third identical circle around A and then proceed to draw the perpendicular bisector.
Finally we will go ahead and plot the circumcenter where we can find the fire pit.
As we can see, the circumcenter is approximately at x=7 and y=7.
