A building is in the shape of a regular octagon. Given that the vertices of the octagon lie on the circle , what is the area of the building to the nearest square unit?
The figure below represents a vertical cross-section of a tunnel, where the equation of its circle is , and is the diameter of the circle. If the unit length of the coordinate system is 54 cm, determine the inner height of the tunnel.
If three lampposts can be modeled by the points , , and , write the equation of the circle that passes through these points.