Problem 332. Cyclic quadrilateral, Ratio of diagonals, Similarity

Proposed Problem
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Complete Problem 332
Level: High School, SAT Prep, College geometry

Problem 331. Square, Point on the Inscribed Circle, Tangency Points

Proposed Problem
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Complete Problem 331
Level: High School, SAT Prep, College geometry

Problem 330. Cyclic quadrilateral, Perpendicular diagonals, Area, Circumcenter

Proposed Problem
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Complete Problem 330
Level: High School, SAT Prep, College geometry

Peter Paul Rubens

Peter Paul Rubens (1577 - 1640). Flemish painter, draughtsman and diplomat. He was the most versatile and influential Baroque artist of northern Europe in the 17th century. He is well-known for his Counter-Reformation altarpieces, portraits, landscapes, and history paintings of mythological and allegorical subjects.

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Peter Paul Rubens Index

Rubens: Portrait of Susanne Fourment

Golden Rectangle
Peter Paul Rubens (1577 - 1640). Flemish painter, draughtsman and diplomat. He was the most versatile and influential Baroque artist of northern Europe in the 17th century. He is well-known for his Counter-Reformation altarpieces, portraits, landscapes, and history paintings of mythological and allegorical subjects.

Susanna Fourment was related by marriage to Rubens' first wife, Isabella Brant. Later the widowed Rubens married Susanna's sister Helena Fourment.

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Portrait of Susanne Fourment by Peter Paul Rubens

Rubens: Self-portrait with Isabella Brant

Golden Rectangle
Peter Paul Rubens (1577 - 1640). Flemish painter, draughtsman and diplomat. He was the most versatile and influential Baroque artist of northern Europe in the 17th century. He is well-known for his Counter-Reformation altarpieces, portraits, landscapes, and history paintings of mythological and allegorical subjects.

Click the figure below to see the interactive illustration of Self-portrait with Isabella Brant by Peter Paul Rubens.



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Self-portrait with Isabella Brant by Peter Paul Rubens

Rubens: Portrait of Isabella Brant

Golden Rectangle
Peter Paul Rubens (1577 - 1640). Flemish painter, draughtsman and diplomat. He was the most versatile and influential Baroque artist of northern Europe in the 17th century. He is well-known for his Counter-Reformation altarpieces, portraits, landscapes, and history paintings of mythological and allegorical subjects.

Click the figure below to see the interactive illustration of Portrait of Isabella Brant by Peter Paul Rubens.



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Portrait of Isabella Brant by Peter Paul Rubens

Rubens: Dance of the Villagers

Golden Rectangle
Peter Paul Rubens (1577 - 1640). Flemish painter, draughtsman and diplomat. He was the most versatile and influential Baroque artist of northern Europe in the 17th century. He is well-known for his Counter-Reformation altarpieces, portraits, landscapes, and history paintings of mythological and allegorical subjects.

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Dance of the Villagers by Peter Paul Rubens

Peter Paul Rubens: The Kermesse

Golden Rectangle
Peter Paul Rubens (1577 - 1640). Flemish painter, draughtsman and diplomat. He was the most versatile and influential Baroque artist of northern Europe in the 17th century. He is well-known for his Counter-Reformation altarpieces, portraits, landscapes, and history paintings of mythological and allegorical subjects.

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The Kermesse by Peter Paul Rubens and the Golden Rectangle

Problem 329. Triangle, Altitudes, Circle, Diameter, Concyclic points

Proposed Problem
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Complete Problem 329
Level: High School, SAT Prep, College geometry

Refuge by Paul Klee

Golden Rectangles

Paul Klee was a Swiss-German artist known for the fine lines and playful geometry in his childlike watercolors and illustrations.
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Refuge by Paul Klee

Wassily Kandinsky: Black and Violet (1923)

Golden Rectangles

Wassily Kandinsky (16 December 1866 - 13 December 1944) was a Russian painter, printmaker and art theorist. One of the most famous 20th-century artists, he is credited with painting the first modern abstract works.
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Black and Violet (1923) by Wassily Kandinsky

Problem 328. Triangle, Incircle, Tangency Points, Parallel, Midpoint

Proposed Problem
Click the figure below to see the complete problem 328 about Triangle, Incircle, Tangency Points, Parallel, Midpoint.


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Complete Problem 328
Level: High School, SAT Prep, College geometry

Tangential or Circumscribed Quadrilateral, Diagonals, Altitudes Theorem

Click the figure below to see the complete Tangential or Circumscribed Quadrilateral: Diagonals, Altitudes Theorem.


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Tangential or Circumscribed Quadrilateral: Diagonal, Altitudes Theorem.
Level: High School, SAT Prep, College geometry

Problem 327. Right triangle Area, Incircle, Circumcircle, Square

Proposed Problem
Click the figure below to see the complete problem 327 about Right triangle Area, Incircle, Circumcircle, Square.


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Complete Problem 327
Level: High School, SAT Prep, College geometry

Problem 326. Equilateral triangle, Semicircle, Equal arcs

Proposed Problem
Click the figure below to see the complete problem 326 about Equilateral triangle, Semicircle, Equal arcs.


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Complete Problem 326
Level: High School, SAT Prep, College geometry

Tangential or Circumscribed Quadrilateral: Diagonals, Inradii Theorem.

Click the figure below to see the complete Tangential or Circumscribed Quadrilateral: Diagonals, Inradii Theorem.


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Tangential or Circumscribed Quadrilateral: Diagonals, Inradii Theorem.
Level: High School, SAT Prep, College geometry

Tangential or Circumscribed Quadrilateral

Theorems and Problems
Click the figure below to see the complete Tangential or Circumscribed Quadrilateral Index.


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Tangential or Circumscribed Quadrilateral Index
Level: High School, SAT Prep, College geometry

Tangential or Circumscribed Quadrilateral: Pitot Theorem

Click the figure below to see the complete Tangential or Circumscribed Quadrilateral: Pitot Theorem.


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Tangential or Circumscribed Quadrilateral: Pitot Theorem
Level: High School, SAT Prep, College geometry

Six Tangential or Circumscribed Quadrilaterals Theorem

Click the figure below to see the complete Six Tangential or Circumscribed Quadrilaterals Theorem.


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Six Tangential or Circumscribed Quadrilaterals Theorem
Level: High School, SAT Prep, College geometry

Problem 325. Isosceles triangle, Altitude, Incircle, Excircle

Proposed Problem
Click the figure below to see the complete problem 325 about Isosceles triangle, Altitude, Cevian, Incircle, Excircle with equal radius.


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Complete Problem 325
Level: High School, SAT Prep, College geometry

Problem 324: Quadrilateral, Perpendicular diagonals, Concurrence

Proposed Problem
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Complete Problem 324
Level: High School, SAT Prep, College geometry

Famous Inventors Mind Map

Graphic organizers are visual representations of knowledge, concepts or ideas.
Click the figure below to see the Famous Inventors Interactive Mind Map based on Time Magazine.


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Famous Inventors Mind Map

Apollo's 11 launch and Golden Rectangles

NASA, ESA celebrates 40th anniversary of Apollo 11's launch

On July 16, 1969, exactly 40 years ago, the Saturn V rocket with the Apollo 11 mission on board was launched from Kennedy Space Center in Cape Canaveral, Florida.
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Apollo 11's launch and Golden Rectangles

Best Inventions of 2008 Mind Map

Graphic organizers are visual representations of knowledge, concepts or ideas.
Click the figure below to see the Best Inventions of 2008 Interactive Mind Map based on TIME's Best Inventions of 2008.


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Best Inventions of 2008

Problem 323: Triangle, Incenter, Circumcenter, Equal circles, Collinearity

Proposed Problem
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Complete Problem 323
Level: High School, SAT Prep, College geometry

Mathematica: Wolfram Demonstrations Project

Video
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Mathematica: Wolfram Demonstrations Project

Mathematica: Creating an Application in 60 Seconds

Video
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Creating an Application in 60 Seconds with Mathematica

Problem 322: Square, Inscribed circle, Tangent, Triangle area

Proposed Problem
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Complete Problem 322
Level: High School, SAT Prep, College geometry

Problem 321: Triangle, Incenter, Excircle, Altitude, Collinearity

Proposed Problem
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Complete Problem 321
Level: High School, SAT Prep, College geometry

Problem 320: Triangle, Circumcircle, Incenter, Excenter, Collinear points

Proposed Problem
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Complete Problem 320
Level: High School, SAT Prep, College geometry

Problem 319: Triangle, Altitudes, Perpendiculars, Collinear points

Proposed Problem
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Complete Problem 319
Level: High School, SAT Prep, College geometry

Problem 318: Scalene triangle, Altitudes, Collinear points

Proposed Problem
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Complete Problem 318
Level: High School, SAT Prep, College geometry

Problem 317: Right triangle and Inscribed Squares

Proposed Problem
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Complete Problem 317
Level: High School, SAT Prep, College geometry

ISO Standards Interactive Mind Map

Graphic organizers are visual representations of knowledge, concepts or ideas.
Click the figure below to see the ISO Standards Interactive Mind Map.


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ISO Standards Interactive Mind Map

Collinear Points, Theorems and Problems

Index
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Collinear Points, Theorems and Problems
Level: High School, SAT Prep, College geometry

Problem 316: Circular segments and Inscribed Squares

Proposed Problem
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Complete Problem 316
Level: High School, SAT Prep, College geometry

Sacred Geometry: Mandala

Sacred Geometry
Click the figure below to see Tibetan 'Five Deity Mandala', 17th Century, and Golden Rectangles.


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Tibetan 'Five Deity Mandala', 17th Century
Sacred Geometry

Theseus and the Minotaur Labyrinth

Sacred Geometry
Click the figure below to see 'Theseus and the Minotaur Labyrinth' and Golden Rectangles.


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Theseus and the Minotaur Labyrinth
Sacred Geometry

Problem 315: Three tangent circles, Common external tangent line, Geometric Mean

Proposed Problem
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Complete Problem 315
Level: High School, SAT Prep, College geometry

Geometric Mean, Theorems and Problems

Index
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Geometric Mean, Theorems and Problems
Level: High School, SAT Prep, College geometry

Arithmetic Mean, Geometric Mean, Harmonic Mean, Root Mean Square

Proposed Problem
Click the figure below to see the geometric illustration of Arithmetic Mean, Geometric Mean, Harmonic Mean, Root Mean Square.


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Arithmetic Mean, Geometric Mean, Harmonic Mean, Root Mean Square
Level: High School, SAT Prep, College geometry

Problem 314. Tangent circles, Common external tangent line, Geometric Mean.

Proposed Problem
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Complete Problem 314
Level: High School, SAT Prep, College geometry

FDA/USFDA Mind Map based on FDA.gov

The Food and Drug Administration (FDA) is an agency of the United States Department of Health and Human Services and is responsible for regulating and supervising the safety of foods, dietary supplements, drugs, vaccines, biological medical products, blood products, medical devices, cosmetics, veterinary products, and radiation-emitting devices.

Graphic organizers are visual representations of knowledge, concepts or ideas.

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Mind Map based on FDA.gov

Geometry Expressions Mind Map

Graphic organizers are visual representations of knowledge, concepts or ideas.
Click the figure below to see the Geometry Expressions Help Interactive Mind Map.


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Geometry Expressions Help Mind Map

Problem 313. Circle, Chord, Tangent, Perpendicular, Geometric Mean

Proposed Problem
Click the figure below to see the complete problem 313.


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Complete Problem 313
Level: High School, SAT Prep, College geometry