Euclidean geometry | Theorems about triangles and circles
In geometry, the equal incircles theorem derives from a Japanese Sangaku, and pertains to the following construction: a series of rays are drawn from a given point to a given line such that the inscribed circles of the triangles formed by adjacent rays and the base line are equal. In the illustration the equal blue circles define the spacing between the rays, as described. The theorem states that the incircles of the triangles formed (starting from any given ray) by every other ray, every third ray, etc. and the base line are also equal. The case of every other ray is illustrated above by the green circles, which are all equal. From the fact that the theorem does not depend on the angle of the initial ray, it can be seen that the theorem properly belongs to analysis, rather than geometry, and must relate to a continuous scaling function which defines the spacing of the rays. In fact, this function is the hyperbolic sine. The theorem is a direct corollary of the following lemma: Suppose that the nth ray makes an angle with the normal to the baseline. If is parameterized according to the equation, , then values of , where and are real constants, define a sequence of rays that satisfy the condition of equal incircles, and furthermore any sequence of rays satisfying the condition can be produced by suitable choice of the constants and . (Wikipedia).
Geometry - What is the triangle bisector theorem
👉 Learn how to solve with similar triangles. Two triangles are said to be similar if the corresponding angles are congruent (equal). Note that two triangles are similar does not imply that the length of the sides are equal but the sides are proportional. Knowledge of the length of the side
From playlist Similar Triangles
Using a set of points to determine if two triangles are similar to each other
👉 Learn how to determine whether two triangles are similar given the coordinate points of the vertices of the triangle. Two triangles are said to be equal when the corresponding angles of the triangles are congruent (equal) or when the corresponding side lengths are proportional. When give
From playlist Similar Triangles
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
Similar Triangles Using Side-Side-Side and Side-Angle-Side
This video explains how to determine if two triangles are similar using SSS and SAS. Complete Video List: http://www.mathispower4u.yolasite.com
From playlist Similarity
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
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
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
Given two similar triangles determine the values of x and y for the angles
👉 Learn how to solve with similar triangles. Two triangles are said to be similar if the corresponding angles are congruent (equal). Note that two triangles are similar does not imply that the length of the sides are equal but the sides are proportional. Knowledge of the length of the side
From playlist Similar Triangles
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
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
What is the similarity of triangles for SSS
👉 Learn how to solve with similar triangles. Two triangles are said to be similar if the corresponding angles are congruent (equal). Note that two triangles are similar does not imply that the length of the sides are equal but the sides are proportional. Knowledge of the length of the side
From playlist Similar Triangles
Finding the missing value using similarity in triangles
👉 Learn how to solve with similar triangles. Two triangles are said to be similar if the corresponding angles are congruent (equal). Note that two triangles are similar does not imply that the length of the sides are equal but the sides are proportional. Knowledge of the length of the side
From playlist Similar Triangles
How to use the triangle bisector theorem to solve your missing length
👉 Learn how to solve with similar triangles. Two triangles are said to be similar if the corresponding angles are congruent (equal). Note that two triangles are similar does not imply that the length of the sides are equal but the sides are proportional. Knowledge of the length of the side
From playlist Similar Triangles
Using angle bisector theorem to determine missing length of a triangle
👉 Learn how to solve with similar triangles. Two triangles are said to be similar if the corresponding angles are congruent (equal). Note that two triangles are similar does not imply that the length of the sides are equal but the sides are proportional. Knowledge of the length of the side
From playlist Similar Triangles
How To Solve The Shape-Shifting Triangle
This delightful problem comes from a German math competition. What's the perimeter of the triangle CDE? You have 3 minutes to solve this problem. Watch the video for a solution, and to see the shape-shifting triangle hidden in this problem. Sources https://puzzling.stackexchange.com/quest
From playlist Math Puzzles, Riddles And Brain Teasers
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
Identifying congruent parts between two polygons
👉 Learn how to solve with similar polygons. Two polygons are said to be similar if the corresponding angles are congruent (equal). When two polygons are similar the corresponding sides are proportional. Knowledge of the length of the sides or the proportion of the side lengths of one of th
From playlist Congruent Polygons
How to write a proportion of lengths and corresponding angles for two triangles
👉 Learn how to solve with similar triangles. Two triangles are said to be similar if the corresponding angles are congruent (equal). Note that two triangles are similar does not imply that the length of the sides are equal but the sides are proportional. Knowledge of the length of the side
From playlist Similar Triangles
Review of triangle properties | 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/triangle-property-review/v/review-of-triangle-properties Comparing perpendicular bisectors to angle bisectors to medians to alti
From playlist Special properties and parts of triangles | Geometry | Khan Academy