Problem 563: Regular Pentagon, Center, Rectangle, Diagonals, Angle

Geometry Problem
Click the figure below to see the complete problem 563.


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Geometry Problems 421 -430

Ten Geometry Problems
Click the figure below to see problems 421-430 about: Right Triangle, Regular Pentagon, Cevian, Angles, Measurement, 30 Degrees, Congruence, Circumcircle, Circumcenter, Altitude, Circumradius, Quadrant, Area.

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Level: High School, College geometry

Geometry Problems 341 - 350

Ten Geometry Problems
Click the figure below to see problems 341-350 about Triangle, Quadrilateral, Pentagon, Hexagon, Inscribed circle, Tangent, Semiperimeter, Equal circles, Concurrent lines, Altitude, Concyclic, Cevian, Incircle.

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Level: High School, SAT Prep, College geometry

Geometry Problems 261-270: Regular Polygon, Pentagon, Hexagon, Circle, Tangent, Similarity, Triangle, Hypotenuse, Catheti, Geometric Mean, Altitude,

Ten Geometry Problems
Click the figure below to see problems 261-270 about Regular Polygon, Pentagon, Hexagon, Circle, Distance, Triangle, Hypotenuse, Catheti, Similarity, Geometric Mean, Altitude, Perpendicular, Projection, Tangent, Fractional Exponent, Common External Tangent.

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Level: High School, SAT Prep, College geometry

Problem 533: Euclid's Elements Book XIII, Proposition 10

Geometry Problem
Click the figure below to see the complete problem 533 about the sides of the regular pentagon, regular hexagon and regular decagon inscribed in the same circle.


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Complete Problem 533

Level: High School, SAT Prep, College geometry

Geometry Problems 161-170: Area, Triangle, Parallelogram, Trapezoid, Pentagon, Octagon

Ten Geometry Problems
Click the figure below to see problems 161-170 about Area, Triangle, Parallelogram, Trapezoid, Pentagon, Diagonal, Midpoint, Octagon.

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Problems 161-170

Level: High School, SAT Prep, College geometry

Bidding Afghanistan up

After the silliness noted earlier this week about the one trillion dollars worth of mineral suddenly discovered in Afghanistan, this morning brought an extra side order of VerySilly. AP reports that the minerals found lying around there are now worth THREE TRILLION, so it must be worth all those deaths and continuing with an unwinnable war, right?

It really makes you wonder just how stupid a) the US military is and b) how stupid the US military thinks the world is. Meanwhile, this humble scribe loved the breathless bit about how the Afghan officials are off to London next week to pitch the iron ore deposits to the Brits. After all, it was a Brit who found them in the first place.....169 years ago. Here's a quote:

"The quality of the ore is excellent, and the richest varieties are to be found," a surveyor wrote in a report on Afghanistan’s untapped natural resources.

The surveyor was one Captain Drummond, a British officer in the 3rd Light Cavalry. The year? 1841.

It's gonna be big news to the limeys, for sure. Meanwhile, if The Hawaiian really wants to know about the mineral wealth of Afghanistan, he should stop listening to the USGS and phone up Hunter Dickinson and ask them all about it. After all, it was HD who got kicked out of the country when the Chinese muscled in on the copper there.

Pentagon Word Cloud and News

Word cloud or tag cloud is a graphical representation of word frequency.
Click the figure below to see the Word Cloud of a Pentagon.



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Pentagon Word Cloud and News

Problem 430: Circumscribed and Inscribed Regular Pentagon, Perpendicular, Areas

Proposed Problem
Click the figure below to see the complete problem 430 about Circumscribed and Inscribed Regular Pentagon, Perpendicular, Areas.


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Complete Problem 430

Level: High School, SAT Prep, College geometry

Problem 429: Circumscribed and Inscribed Regular Pentagon, Perpendicular, Measurement

Proposed Problem
Click the figure below to see the complete problem 429 about Circumscribed and Inscribed Regular Pentagon, Perpendicular, Measurement.


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Complete Problem 429

Level: High School, SAT Prep, College geometry

Problem 410: Two Regular Pentagons, Angle

Proposed Problem
Click the figure below to see the complete problem 410 about Two Regular Pentagons, Angle.


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Complete Problem 410
Level: High School, SAT Prep, College geometry

Problem 342. Pentagon, Inscribed Circle, Tangent, Semiperimeter

Proposed Problem
Click the figure below to see the complete problem 342 about Pentagon, Inscribed Circle, Tangent, Semiperimeter.


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Complete Problem 342
Level: High School, SAT Prep, College geometry

Problem 261: Regular Pentagon inscribed in a circle, sum of distances

Proposed Problem


See complete Problem 261 at:
gogeometry.com/problem/p261_regular_pentagon_inscribed_circle_distance.htm

Level: High School, SAT Prep, College geometry

Post your solutions or ideas in the comments.

Pentagon Index

Theorems and Problems



See complete Pentagon Index at:
http://www.gogeometry.com/geometry/pentagon_polygon_shape_index_5_sides.html

Level: High School, SAT Prep, College geometry

Post your solutions or ideas in the comments.

Archimedes' Book of Lemmas, Proposition #15

Problem 655: Inscribed Regular Pentagon, Arc, Midpoint, Perpendicular, Radius
Exercise your brain. Archimedes wrote the "Book of Lemmas" more than 2200 years ago. Solve the proposition #15 (high school level) and lift up your geometry skills.

Click the figure below to see the complete problem 655


Continue reading at:
gogeometry.com/ArchBooLem15.htm

Miquel Pentagram, Dynamic Geometry

Requires Java 1.3 or higher and Java enable browser
Take a pentagram ABCDE forming a convex pentagon FGHIJ and triangles AFJ, BGF, CHG, DIH, and EJI. Construct the circumcircles of triangles AFJ, BGF, CHG, DIH, and EJI. Then the five new points, K,L,M,N,P resulting from the intersection of two consecutive circumferences are concyclic (lie on the same circumference).



Continue exploring at:
gogeometry.com/javacar/Miquel_1.htm

Elearn Geometry Problem 169

See complete Problem 169 at:
www.gogeometry.com/problem/p169_parallelogram_triangle_pentagon_area.htm

Parallelogram, Interior and Exterior Points, Diagonals, Pentagon, Triangles, Areas. Level: High School, SAT Prep, College geometry

Post your solutions or ideas in the comments.

Elearn Geometry Problem 168

See complete Problem 168 at:
www.gogeometry.com/problem/p168_parallelogram_triangle_pentagon_area.htm

Parallelogram, Diagonals, Pentagon, Triangles, Areas. Level: High School, SAT Prep, College geometry

Post your solutions or ideas in the comments.