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Circles and Segments

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Circles and Segments

These four parts are designed to support students in making connections between chord, secant, and tangent line relationships in circles and creating proofs of these relationships using triangle similarity.

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Circles and Squares

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Circles and Squares

In this task, you must solve a problem about circles inscribed in squares.

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Formulas Involving Arc Length

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Formulas Involving Arc Length

Connect visuals to arc length formulas involving the size of an angle.

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Inscribing a Triangle in a Circle

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Inscribing a Triangle in a Circle

This problem introduces the circumcenter of a triangle and shows how it can be used to inscribe the triangle in a circle. It also shows that there cannot be more than one circumcenter. 

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Right Triangles Inscribed in Circles 1

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Right Triangles Inscribed in Circles 1

This task provides a good opportunity to use isosceles triangles and their properties to show an interesting and important result about triangles inscribed in a circle with one side of the triangle a diameter: the fact that these triangles are always right triangles is often referred to as Thales' theorem. It does not have a lot of formal prerequisites, just the knowledge that the sum of the three angles in a triangle is 180 degrees.

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Right Triangles Inscribed in Circles 2

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Right Triangles Inscribed in Circles 2

The result here complements the fact, presented in the task ''Right triangles inscribed in circles I,'' that any triangle inscribed in a circle with one side being a diameter of the circle is a right triangle. A second common proof of this result rotates the triangle by 180 degrees about M and then shows that the quadrilateral, obtained by taking the union of these two triangles, is a rectangle. 

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Temple Geometry

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Temple Geometry

During the Edo period (1603-1867) of Japanese history, geometrical puzzles were hung in the holy temples as offerings to the gods and as challenges to worshippers.
Here is one such problem for you to investigate.

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