Circles defined for a triangle
In geometry, the incircle or inscribed circle of a triangle is the largest circle that can be contained in the triangle; it touches (is tangent to) the three sides. The center of the incircle is a triangle center called the triangle's incenter. An excircle or escribed circle of the triangle is a circle lying outside the triangle, tangent to one of its sides and tangent to the extensions of the other two. Every triangle has three distinct excircles, each tangent to one of the triangle's sides. The center of the incircle, called the incenter, can be found as the intersection of the three internal angle bisectors. The center of an excircle is the intersection of the internal bisector of one angle (at vertex A, for example) and the external bisectors of the other two. The center of this excircle is called the excenter relative to the vertex A, or the excenter of A. Because the internal bisector of an angle is perpendicular to its external bisector, it follows that the center of the incircle together with the three excircle centers form an orthocentric system. but not all polygons do; those that do are tangential polygons. See also tangent lines to circles. (Wikipedia).
A satisfying geometry question - circle exterior to a triangle side
Thanks to Amit from India for the suggestion! A circle is tangent on the exterior of a side of a triangle and tangent to the lines through the other two sides. The tangent side length 7, and the other side lengths are 8 and 9. What is the radius of the circle? 0:00 Problem 1:22 Geometry 5
From playlist Math Puzzles, Riddles And Brain Teasers
👉 Learn the essential definitions of triangles. A triangle is a polygon with three sides. Triangles are classified on the basis of their angles or on the basis of their side lengths. The classification of triangles on the bases of their angles are: acute, right and obtuse triangles. The cl
From playlist Types of Triangles and Their Properties
Incenter, Circumcenter, Orthocenter & Centroid of a Triangle - Geometry
This geometry video tutorial explains how to identify the location of the incenter, circumcenter, orthocenter and centroid of a triangle. The incenter can be found be drawing the 3 angle bisectors of a triangle and identifying the point of intersection. The incenter always lie inside of
From playlist Geometry Video Playlist
👉 Learn the essential definitions of triangles. A triangle is a polygon with three sides. Triangles are classified on the basis of their angles or on the basis of their side lengths. The classification of triangles on the bases of their angles are: acute, right and obtuse triangles. The cl
From playlist Types of Triangles and Their Properties
Incenter and incircles of a triangle | Geometry | Khan Academy
Using angle bisectors to find the incenter and incircle of a triangle Watch the next lesson: https://www.khanacademy.org/math/geometry/triangle-properties/angle_bisectors/v/inradius-perimeter-and-area?utm_source=YT&utm_medium=Desc&utm_campaign=Geometry Missed the previous lesson? https:
From playlist Special properties and parts of triangles | Geometry | Khan Academy
Unknown identities of known shapes by Swati Sircar
PROGRAM : SUMMER SCHOOL FOR WOMEN IN MATHEMATICS AND STATISTICS ORGANIZERS : Siva Athreya and Anita Naolekar DATE : 13 May 2019 to 24 May 2019 VENUE : Ramanujan Lecture Hall, ICTS Bangalore The summer school is intended for women students studying in first year B.A/B.Sc./B.E./B.Tech.
From playlist Summer School for Women in Mathematics and Statistics 2019
What is an equilateral triangle
👉 Learn the essential definitions of triangles. A triangle is a polygon with three sides. Triangles are classified on the basis of their angles or on the basis of their side lengths. The classification of triangles on the bases of their angles are: acute, right and obtuse triangles. The cl
From playlist Types of Triangles and Their Properties
Inradius, perimeter, and area | Special properties and parts of triangles | Geometry | Khan Academy
Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/math/geometry-home/triangle-properties/angle-bisectors/v/inradius-perimeter-and-area Showing that area is equal to inradius times semiperimeter Watch the next lesson:
From playlist Special properties and parts of triangles | Geometry | Khan Academy
Triangle Area from Inradius and Semiperimeter (visual proof)
This is a short, animated visual proof showing that the area of a triangle is given by the product of the inradius and the semiperimeter of the triangle. #manim #math #mathvideo #mathshorts #geometry #circle #triangle #animation #theorem #pww #proofwithoutwords #visualproof #proof #incirc
From playlist Algebra
Heron’s formula: What is the hidden meaning of 1 + 2 + 3 = 1 x 2 x 3 ?
Today's video is about Heron's famous formula and Brahmagupta's and Bretschneider's extensions of this formula and what these formulas have to do with that curious identity 1+2+3=1x2x3. 00:00 Intro 01:01 1+2+3=1x2x3 in action 02:11 Equilateral triangle 02:30 Golden triangle 03:09 Chapter
From playlist Recent videos
What is an equiangular triangle
👉 Learn the essential definitions of triangles. A triangle is a polygon with three sides. Triangles are classified on the basis of their angles or on the basis of their side lengths. The classification of triangles on the bases of their angles are: acute, right and obtuse triangles. The cl
From playlist Types of Triangles and Their Properties
We give a solution to question A2 from the 2019 William Lowell Putnam Mathematics Competition. http://www.michael-penn.net http://www.randolphcollege.edu/mathematics/
From playlist Putnam Exam Solutions
The Incenter (X1) is the meet of the interior angle bisectors (which I like to call bilines). It is the first point on Clark Kimberling's list of triangle centers at the Enyclopedia of Triangle Centers, from which this Geometer's SKetchpad worksheet is taken. It is important to note that
From playlist Triangle Geometry
Introduction to the Interior and Exterior Angles of a Triangle.
Complete videos list: http://mathispower4u.yolasite.com/ This video will define the interior and exterior angles of a triangle and then state several theorems involving the interior and exterior angles of a triangle.
From playlist Triangles and Congruence
👉 Learn the essential definitions of triangles. A triangle is a polygon with three sides. Triangles are classified on the basis of their angles or on the basis of their side lengths. The classification of triangles on the bases of their angles are: acute, right and obtuse triangles. The cl
From playlist Types of Triangles and Their Properties
Inradius of a Right Triangle (visual proof)
This is a short, animated visual proof of two different formulas for the inradius of a right triangle in terms of its side lengths. #manim #math #mathvideo #mathshorts #geometry #circle #triangle #animation #theorem #pww #proofwithoutwords #visualproof #proof #incircle #inradius #righttri
From playlist Geometry
Triangle Geometry Old and New: An introduction to Hyperbolic Triangle Geometry
We present a very brief survey of a few classical results in Euclidean triangle geometry, and then give an introduction to triangle geometry in the new setting of universal hyperbolic geometry. This occurs in a projective Beltrami Klein model involving both the inside and outside of a dist
From playlist MathSeminars
👉 Learn the essential definitions of triangles. A triangle is a polygon with three sides. Triangles are classified on the basis of their angles or on the basis of their side lengths. The classification of triangles on the bases of their angles are: acute, right and obtuse triangles. The cl
From playlist Types of Triangles and Their Properties
Incentre of a triangle using Inkscape
How to precisely construct the incentre and incircle of a triangle using Inkscape. This method pays homage to the old compass and straight edge constructions of years gone by. The Inkscape file of the completed drawing may be found by clicking "Geoff's Inkscape files" on the main page at
From playlist Inkscape for teachers