Theorems about quadrilaterals and circles | Euclidean plane geometry
In geometry, the Japanese theorem states that the centers of the incircles of certain triangles inside a cyclic quadrilateral are vertices of a rectangle. Triangulating an arbitrary cyclic quadrilateral by its diagonals yields four overlapping triangles (each diagonal creates two triangles). The centers of the incircles of those triangles form a rectangle. Specifically, let □ABCD be an arbitrary cyclic quadrilateral and let M1, M2, M3, M4 be the incenters of the triangles △ABD, △ABC, △BCD, △ACD. Then the quadrilateral formed by M1, M2, M3, M4 is a rectangle. Note that this theorem is easily extended to prove the Japanese theorem for cyclic polygons. To prove the quadrilateral case, simply construct the parallelogram tangent to the corners of the constructed rectangle, with sides parallel to the diagonals of the quadrilateral. The construction shows that the parallelogram is a rhombus, which is equivalent to showing that the sums of the radii of the incircles tangent to each diagonal are equal. The quadrilateral case immediately proves the general case by induction on the set of triangulating partitions of a general polygon. (Wikipedia).
Circle Theorem Proof - Cyclic Quadrilaterals
A proof of the cyclic quadrilateral Theorem, one of the circle theorems proofs!
From playlist Circle Theorem Proofs
The Cyclic quadrilateral quadrea theorem (cont.) | Rational Geometry Math Foundations 127b
The Cyclic quadrilateral quadrea (CQQ) theorem is a major re-evaluation of the classical theorem of Brahmagupta on the area of a convex cyclic quadrilateral, which combines it with Robbins much more recent formula for the corresponding area of a non-convex cyclic quadrilateral. We exhibit
From playlist Math Foundations
Determine if a set of points is a parallelogram using the distance formula
👉 Learn how to determine the figure given four points. A quadrilateral is a polygon with four sides. Some of the types of quadrilaterals are: parallelogram, square, rectangle, rhombus, kite, trapezoid, etc. Each of the types of quadrilateral has its properties. Given four points that repr
From playlist Quadrilaterals on a Coordinate Plane
Circle Theorems: Cyclic Quadrilateral (Grade 6) - OnMaths GCSE Maths Revision
Topic: Circle Theorems: Cyclic Quadrilateral Do this paper online for free: https://www.onmaths.com/circle-theorems/ Grade: 6 This question appears on calculator and non-calculator higher GCSE papers. Practise and revise with OnMaths. Go to onmaths.com for more resources, like predicted G
From playlist Circle Theorems
Suggest a problem: https://forms.gle/ea7Pw7HcKePGB4my5 Please Subscribe: https://www.youtube.com/michaelpennmath?sub_confirmation=1 Patreon: https://www.patreon.com/michaelpennmath Merch: https://teespring.com/stores/michael-penn-math Personal Website: http://www.michael-penn.net Randolp
From playlist Geometry
Determine if a set of points is a parallelogram by using the slope formula
👉 Learn how to determine the figure given four points. A quadrilateral is a polygon with four sides. Some of the types of quadrilaterals are: parallelogram, square, rectangle, rhombus, kite, trapezoid, etc. Each of the types of quadrilateral has its properties. Given four points that repr
From playlist Quadrilaterals on a Coordinate Plane
Determining if a set of points makes a parallelogram or not
👉 Learn how to determine the figure given four points. A quadrilateral is a polygon with four sides. Some of the types of quadrilaterals are: parallelogram, square, rectangle, rhombus, kite, trapezoid, etc. Each of the types of quadrilateral has its properties. Given four points that repr
From playlist Quadrilaterals on a Coordinate Plane
The circumquadrance of a cyclic quadrilateral|Rational Geometry Math Foundations 149 | NJ Wildberger
Around 1400, the mathematician Parameshvara from the southern Indian state of Kerala discovered a remarkable formula in the spirit of Brahmagupta, but which gives the circumradius of a cyclic quadrilateral in terms of the four lengths of sides, at least if the quadrilateral is convex. In t
From playlist Math Foundations
In this lesson we discuss how opposite angles in cyclic quadrilaterals will sum 180 degrees, as well as the theorem that the tangent line to a circle will make a 90 degree angle to the radius at the point of contact.
From playlist Mathematics Lessons, Grades 8-10, High School, Australia
How to do Circle Theorems A/A* GCSE Higher Maths Worked Exam paper revision, practice & help
7 Questions on Circle theorems aimed at Edexcel / AQA GCSE Maths Exam paper revision for higher grade A/A* Students. Timings for questions Qu 2 - https://www.youtube.com/watch?v=Trkt68IjRpg#t=1m42s Qu 3 - https://www.youtube.com/watch?v=Trkt68IjRpg#t=3m07s Only do question 4 and 5 if you h
From playlist A/A* Topic Based GCSE Exam Question revision
Circle Theorems 2 (GCSE Higher Maths)- Exam Qs 14
Powered by https://www.numerise.com/ This video is a tutorial on Circle Theorems Questions. You should have already watched the Circle Theorems 1 Tutorial 13. This video is for students attempting the Higher paper AQA Unit 3 Maths GCSE, who have previously sat the foundation paper. Expla
From playlist AQA Unit 3 Maths GCSE Higher Revision Course
Geometry (Geometric Proofs) Ultimate revision guide for Further maths GCSE
Ultimate Guide to Further maths GCSE Geometry (Geometric Proofs) (level 2 Qualification from AQA) 1. Number - https://www.youtube.com/watch?v=ciR2OfUdO0g&list=PL2De0DVeFj3UQsVP217m4432peZ7Jow6r&index=19 2. Algebra - https://www.youtube.com/watch?v=IFqmY9UfAzc&index=2&list=PL2De0DVeFj3UQs
From playlist Ultimate Guide to Further Maths GCSE
Grade 7-9 Circle Theorem Problems - GCSE Higher Maths Revision
Grade 7-9 circle theorem problems for GCSE mathematics questions from the video: https://bit.ly/2xrP8pe
From playlist Geometry Revision
Circle Theorems: Angles In Cyclic Quadrilateral (Grade 6) - OnMaths GCSE Maths Revision
Topic: Circle Theorems: Angles In Cyclic Quadrilateral Do this paper online for free: https://www.onmaths.com/circle-theorems/ Grade: 6 This question appears on calculator and non-calculator higher GCSE papers. Practise and revise with OnMaths. Go to onmaths.com for more resources, like p
From playlist Circle Theorems
The projective Quadruple quad formula | Rational Geometry Math Foundations 148 | NJ Wildberger
In this video we introduce the projective version of the Quadruple quad formula, which not only controls the relationship between four projective points, but has a surprising connection with the geometry of the cyclic quadrilateral. The projective quadruple quad function is called R(a,b,
From playlist Math Foundations
All of the Circle Theorems in 10 Minutes!! | Circle Theorem Series Part 1 | GCSE Maths Tutor
A video revising the techniques and strategies for learning each of the circle theorems (Higher Only). This video is part of the Geometry module for Circle Theorems in GCSE maths, see my other videos below to continue with the series. These are the calculators that I recommend: Casio fx
From playlist GCSE Maths Videos
Cyclic Quadrilateral Phenomenon
1 cyclic quadrilateral + 4 perpendiculars = 😮? How to prove? 🤔 Source: Antonio Gutierrez. https://geogebra.org/m/MZ8Zgqsg #GeoGebra #MTBoS #ITeachMath #geometry #math #maths #proof
From playlist Geometry: Challenge Problems
Circle Theorems - Exam Style Questions | Grade 7 Maths Series | GCSE Maths Tutor
A video revising the techniques and strategies for answering exam style questions on circle theorems (Higher Only). This video is part of the Geometry module for Circle Theorems in GCSE maths, see my other videos below to continue with the series. These are the calculators that I recomme
From playlist GCSE Maths Videos
Determine if a set of points makes up a rectangle using the distance formula
👉 Learn how to determine the figure given four points. A quadrilateral is a polygon with four sides. Some of the types of quadrilaterals are: parallelogram, square, rectangle, rhombus, kite, trapezoid, etc. Each of the types of quadrilateral has its properties. Given four points that repr
From playlist Quadrilaterals on a Coordinate Plane