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Geometry 52b Incenter Theorem Inscribed Circles and Angle Bisectors New Version
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The incenter of a triangle is the point of concurrency of it's three angle bisectors. A triangle has three angles, so it has three angle bisectors. The angle bisectors of a triangle are concurrent, which means they intersect at one point. An inscribed circle is a circle placed within a polygon that touches each side of the polygon at one spot. Each side of the polygon is tangent to that circle. The incenter is the center of the circle, no matter what type of triangle it is. The Incenter Theorem states the incenter of a triangle is equidistant from the sides of a triangle. Unlike the circumcenter, the incenter is always inside the triangle. The incenter is the center of the triangle's inscribed circle. We can find the incenter of a triangle by finding where at least two angle bisectors meet, or three for more accuracy. We can construct the angle bisectors with a compass and straightedge (or measure an angle with a protractor and divide the measure by 2). We use properties of angle bisectors to find an unknown angle measure and an unknown distance from the incenter to a side. We solve a word problem that involves finding the incenter of a triangle. • Geometry 5.1a, Perpendicular Bisector Theorem its Converse • • Geometry 5.1a, Perpendicular Bisector... • Geometry 5.1b, Angle Bisector Theorem its Converse • • Geometry 5.1b, Angle Bisector Theorem... • Geometry 5.2a, Circumcenter of a Triangle Circumcenter Theorem • • Geometry 5.2a, Circumcenter of a Tria... • Geometry 5.3a, Centroid Theorem construct Centroid of a Triangle • • Geometry 5.3a, Centroid Theorem con... • Draw with compass straightedge Playlist • • Drawing with a Compass and straightedge • Geometry 1.3, Measuring constructing angles • • Geometry 1.3, Measuring constructin... • High School Geometry Playlist • • High School Geometry Course • Textbook you can use, Holt McDougal Geometry, copyright 2012 • This video and its contents are the property of JoAnn's School and • is protected under U.S. copyright law. • FOLLOW ME: • TWITTER / joannsschool • FACEBOOK Message me! / joannsschool • MINDS Minds.com/joannsschool • SUPPORT MY WORK: • PATREON / joannsschool • YOUTUBE FAN FUNDING / joannsschool • PAYPAL https://www.paypal.me/JoAnnsSchool
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