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Inscribed and Circumscribed Polygons


In these lessons, we will learn about the properties of inscribed polygons and circumscribed polygons. We will also learn how to solve problems involving inscribed quadrilaterals and inscribed triangles.

An inscribed polygon is a polygon in which all vertices lie on a circle.
The polygon is inscribed in the circle and the circle is circumscribed about the polygon.
(It is a polygon in a circle)

inscribed polygon

A circumscribed polygon is a polygon in which each side is a tangent to a circle.
The circle is inscribed in the polygon and the polygon is circumscribed about the circle. (It is a circle in a polygon)

circumscribed polygon

Inscribed and Circumscribed Polygons
A lesson on polygons inscribed in and circumscribed about a circle.
The circumcenter of a polygon is the center of a circle circumscribed about a polygon.
The incenter of a polygon is the center of a circle inscribed in the polygon.
If a quadrilateral is inscribed in a circle, ite opposite angles are supplementary.
If a parallelogram is inscribed in a circle, it must be a rectangle.
Concyclic is a set of points that must all lie on a circle.

Inscribed Quadrilaterals

Square Inscribed in a Circle
The relationship between a circle and an inscribed square.
The diameter of the circle = side of square × square root of 2.
Circles - Inscribed Quadrilaterals
How to find missing angles inside inscribed quadrilaterals.

How to solve problems involving quadrilaterals inscribed in circles.
Inscribed Quadrilaterals
Quadrilaterals inscribed in a circle. Opposite angles are supplementary.

Cyclic Quadrilaterals
In this lesson we looked at properties of cyclic quadrilaterals.

Inscribed Triangles

If an inscribed triangle is a right triangle, then the hypotenuse is the diameter. If an inscribed angle has a diameter as one of its sides, then its a right triangle.

Circles Inscribed in Right Triangles
This problem involves two circles that are inscribed in a right triangle.
The circle with center A has radius 3 and its tangent to both the positive x-axis and the positive y-axis. The circle with center B has radius 1 and is tangent to both the x-axis and the circle with center A. The line L is tangent to both circles. Find the y-intercept of line L.

Rotate to landscape screen format on a mobile phone or small tablet to use the Mathway widget, a free math problem solver that answers your questions with step-by-step explanations.

You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

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