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The city council is planning to construct a park on North Street that has a triangular perimeter. They want to place a fountain at a point equidistant from all three sides of the park. Where should the council place the fountain?. . A. at the point of intersection of the angle bisectors and perpendicular bisectors of the park. . B. at the center of the inscribed circle of the park. . C. at the center of the circumscribed circle of the park. . D. at the point of intersection of the lines perpendicular to two sides of the park. . E. at the point of intersection of the medians of the park

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taskmasters
The council should place the fountain at the center of the inscribed circle of the park. The correct option among all the options that are given in the question is the second option or option "B". I hope that the answer has actually come to your great help.
JeanaShupp

Answer:  B. at the center of the inscribed circle of the park.


Step-by-step explanation:

We know that circumcenter as the point that is equidistant from all three of the vertices of a triangle.

The circumcenter is the center of the circle which goes through the three vertices of the triangle.

Since all radii of a circle are congruent. Therefore, the circumcenter is equidistant from the vertices of the triangle.

Hence, B is the right answer . The council should place the fountain at the center of the inscribed circle of the park such that fountain will be equidistant from all three sides of the park.