Jan 062012
Understanding the mathematical concepts behind inscribed circles and polygons is a necessary concept to master before taking the exam.
•A polygon is said to be inscribed in a circle if all its vertices are points on the circle.
–Note: If the polygon inscribed in the circle is a rectangle, then the diagonals of the rectangle are diameters of the circle.
•A circle is said to be inscribed in a polygon if the circle touches each side of the polygon at exactly one point.
–Note: If the polygon, in which a circle is inscribed, is a square, then each side of the square has the same length as the diameter of the circle.
•A common problem type on SAT Exams is to find the area of shaded regions that involve inscribed circles and polygons. The strategy to solve these types of problems is to first find the area of the outer region, and then subtract the portion that is not shaded.
•Note: Any line tangent to a circle is perpendicular to a radius that is drawn to the point of contact.