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### Course: High school geometry>Unit 8

Lesson 11: Constructing regular polygons inscribed in circles

# Geometric constructions: circle-inscribed square

Sal constructs a square that is inscribed inside a given circle using compass and straightedge. Created by Sal Khan.

## Want to join the conversation?

• how does this construction prove that this square is actually a square
• It begins with a diameter, then constructs the perpendicular bisector of the diameter (by drawing the line through the lemon formed by the overlapping congruent circles placed at the endpoints). These form the diagonals of your quadrilateral.
(1) They bisect each other, because they cross at the center.
(2) They are congruent, since they are both diameters.
(3) They are perpendicular, per construction.

(1) proves it is a parallelogram, (2) that it is a rectangle, and (3) that it is a rhombus. Thus it is proven to be a square.
• difference between polygon and regular polygon
• A polygon is any type of closed figure in which all sides are straight. A regular polygon is a polygon in which all sides are the same length and all angles have the same measure.
• In which website in Khan Academy can i visit to move the compass and straightedge where? does someone know?
• There might be one, but for all I know, It could have been removed.
• How did Sal decide how big the blue circles were at to
• The first circle needs to be at least half the diameter of the circle win the problem. Then, with the second circle, Sal simply placed the midpoint of the new compass on the midpoint of the first circle, made the circles the same size by adjusting the new compass, and then placed the new circle's midpoint on the opposite side of the circle in the problem.
Hope this helps :)
• Why doesn't the site have construction exercises anymore?
• how do we know its an actual square
• Since it is a perpendicular bisectors of equal length that are diameters, each part forms a radius. Since the 90 degree angle is there and the sides are equal, the other angles have to be 45 degress, and each of the 4 triangles have to be similar, so you have angles of 90 degrees total (rectangle requirements) and with perpendicular bisectors and all sides equal (rhombus requirements), it has to be a square.
• which website did you use?
• Sal completed the exercise on the Khan Academy website.
(1 vote)
• In a make up of a circle I notice there are six pentagons within hexagons, is it the curved shap of the circle itself and its angle ? How do you get the five sides of the pentagon to line up with the six sides of the Hexagon?