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Search Results for “circle”

By Nick Halsey
Basic Unit Circle
This very basic representation of the unit circle displays the unit circle with an input for the standard angle θ in degrees (which controls the angle between the hypotenuse and the x axis). The outputs represent the other two sides of the triangle and give their lengths through decimals. A good investigation for geometry students is to have them test out different angles here, then compare the results to those testing the angles with sine and cosine on their calculators. This allows them to visualize the unit circle in a precise diagram rather than simply running inputs and outputs on their calculators.

Tags: Geomtery, Unit-Circle, Sine, Cosine

By Nick Halsey
Epic Circle Trace
A line passes intersects a circle at two points. Each point is located proportionally around the circle in terms of a given function of t. The path of the line’s movement is traced as t varies. Try changing/animating t. Can you figure out how each point is constrained, in terms of t? Look at the gx source file for the answer. Hint: look at the period of the movement, and how it changes as t changes.

Tags: Trace, puzzler, circle, proportional-points, functions

By Duncan
circle intersections
Can you conjecture a formula for the product of the two distances from a point to a circle?

Tags: circle, tangent

By Phil Todd
Circle Equation
Try to match a circle defined by its equation with one defined by its center and a point on the circumference. Drag for a hint.

Tags: circle, equation

By Phil Todd
Circle in a trapezoid
When is it possible to draw a circle tangent to all four sides of a trapezoid?  

Tags: trapezoid, inscribed-circle

By Phil Todd
Circle Involute
Find the area of grass accessible to a goat who is tethered to a circular silo.

Tags: Involute, Circle, Goat

By Andrew Zhao
Euclids Elements - Book 3 - Proposition 14
Creating a tangent on a circle given point A that is outside the circle.

Tags: Euclid, Elements, Geometry, Circle, Tangent

By Duncan
Hypocycloid
Rolling a smaller circle inside a larger one draws a hypocycloid

Tags: Cycloid, curve, circle

By Nick Halsey
Two Circle Trace
This trace follows the position of one circle as it moves along the path of the edge of another.

Tags: Circles, Traces

By Nick Halsey
Chord Angle Theorem
The chord angle theorem states that in an inscribed triangle (ABC) where A is the center of the circle and BC is a chord, and BDC is an inscribed triangle on the same chord, angle BDC must equal one half of angle BAC. Try changing the angle and moving point D and observe the theorem’s truth. Note: the measure of angle BDC is being constantly recalculated as point D is dragged, but it doesn't change because of this theorem.

Tags: Chord, Angle, Theorem, Circle, Draggable, Proof


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