Kris has 3 daughters who all live in different cities across Georgia. She wants to live somewhere that is an equal distance from each of her daughters. She mapped out the 3 cities and drew a triangle connecting them. How can she find a point on the map that is an equal distance from all 3 cities?

She will be able to find a point on the map by constructing a circumference connecting all the 3 points on the triangle. Circumcenter will the the point equal to all the points of the triangle.

What is circumcenter ?

"The circumcenter of a triangle is defined as the point where the perpendicular bisectors of the sides of that particular triangle intersect. In other words, the point of concurrency of the bisector of the sides of a triangle is called the circumcenter. It is denoted by P(X, Y). The circumcenter is also the center of the circumcircle of that triangle and it can be either inside or outside the triangle."

Let the daughter a be living x km away from b.

Let the daughter b be living at y km away from c.

Let the daughter c be living at z km away from the a.

So, the circumcenter will be the center joining all the 3 points at the equal distance.

The circumcenter (X, Y), then the formula is given by,

[tex]D1= \sqrt(X-x1)^2+(Y-y1)^2]\\D2= \sqrt(X-x2)^2+(Y-y2)^2]\\D3= \sqrt(X-x3)^2+(Y-y3)^2][/tex]

Hence, the circumcenter will be the point equidistance to every point.

To know more about circumcenter here

https://brainly.com/question/12661265

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