Question

A water tower is to be built so that it is the same distance from cities X, Y, Z. Draw a sketch on a triangle XYZ to show location of W where the water tower should be built. Justify your sketch using a postulate or theorem.

Answer 1

Circumcentre (the point of intersection of the perpendicular bisectors of all three sides of a triangle) is a point equidistant from any three given non-collinear points.

Answer 2

Hence the circumcenter is the center of a circle that passes through the three vertices.

Answer 3

How do you figure it out? I assume it is the exact center of the triangle?

Answer 4

No it's not necessarily the exact center of the triangle (unless it's an equilateral triangle). It is the center of the circle that can be drawn with each vertex of the triangle as a point on the circle. In fact the cicumcenter can lie outside of the triangle. To find the circumcenter, i). Draw a triangle with vertices X, Y, and Z, ii). measure the length of any side of the triangle with a ruler and mark off the midpoint, iii). draw a straight line that is perpendicular (at right angle) to the side and intersecting at the midpoint (this straight line is your perpendicular bisector), iv). Repeat steps ii) and iii) for each of the remaining sides of the triangle. The point where all three perpendicular bisectors intersect is the location of the circumcenter (the point equidistant from each X, Y, and Z). Hence the location of the tower equidistant from the three cities.