The given figure shows a pulley having a radius of 5 units, and touching the two coordinate axes. It is operated by a wire that passes over a smaller pulley . If the equation of circle of pulley is , and each unit of the coordinate axes represents 4 cm, determine the distance between the centers of the two pulleys.
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 blueprint of a city is in a Cartesian coordinate system, where each unit represents 5 meters. Given that the circle represents one of the city’s squares, determine the area of the square to nearest square meter. Consider .
Find, to the nearest hundredth,the area of the circle .
Determine, to the nearest hundredth, the area of a regular 10-sided polygon, given that the circle passes through its vertices.
A city is divided into regions bounded by circles centered at its city hall building. The first region is within 19 miles of city hall. The next boundary is 19 miles beyond, and so on. Determine the equation of the third circle.
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.
Given that , , and are the centers of three circles whose radii are 8, 10, and 5 length units, respectively, and that length units, find the general form of the equations of circles and .