Inscribed Angles and Arcs including Circumscribed and Inscribed Polygons.

Do you know the differences and similarities between circumscribed and inscribed polygons? Do you know how to deal with arcs formed by arcs intercepted by inscribed angles? Do you know the measure of an inscribed angle intersecting a semicircle?

The focus of this lesson is in presenting to you how to give the right answers to these type of questions. We start by defining inscribed angles in terms of the angular measure of the arc they intersect, and we continue to present a multi step problem that involves inscribed polygons with inscribed angles, and central angles intercepting arcs in the circle. After each example a similar version is given; so you will be presented with a suggested problem to solve, to work it on the screen with your stylus and the marker tools menuĀ” You will find yourself increasingly able to work problems with circles!

Lesson's Content

Lesson In PDF Format (no animations)


Lesson's Glossary

The curved segment that is between two points in the circumference of a circle.

Arc length
The distance between an arc's endpoints along the path of the circle.

Center of a circle
The point that all points in the circle are equidistant from.

Central angle of a circle
An angle whose vertex is the center of the circle.

Circumscribed circle or circumcircle of a polygon: A polygon is circumscribed about a circle if all the sides are tangent to the circle, and a circle is circumscribed about a polygon if all the vertices of this are on the circumference of the circle.

Chord of a circle
A segment whose endpoints are on a circle.

The set of points on a plane at a certain distance (radius) from a certain point (center); a polygon with infinite sides.

Inscribed angle
An inscribed angle is an angle whose vertex is on a circle and whose rays intersect the circle.

Inscribed planar shape or solid: A polygon is inscribed in a circle if the vertices of a polygon inside a circle are on the circumference of the circle; a circle is inscribed to a polygon if all the sides of the polygon are tangent to the circle in the interior of the polygon.

Minor arc
An arc whose endpoints form an angle less than 180 degrees with the center of the circle.

Major arc
An arc whose endpoints form an angle over 180 degrees with the center of the circle.

Plural form of radius.

The segment whose endpoints are any point on a circle or sphere and its center; the length of that segment.

Part of a circle containing its center and an arc.

An arc whose central angle is a right angle.


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