Question

Solve for the unknown angles. Justify your answers. The local church has a triangular-shaped ornamental garden. The parish Council wants to place a statue at a point in the middle that will be an equal distance from, and perpendicular to, each of the three paths that border the garden. Describe to them how they can find this point, with a diagram to support your answer.

Answer 1

The statue should be placed at the circumcentre of the triangle.

Explanation:

The circumcentre of a triangle is the point that is formed by the intersection of the three perpendicular bisectors of each of the three sides.

This point is equidistant from all the three sides and is perpendicular to the three sides.

So, to place the statue, the parish Council can draw perpendicular bisectors for each sides and the intersection of these perpendicular bisectors would be the point where the statue can be placed.

Consider the diagram below.

Point P is the circumcentre of the triangle.