Euclid's Muse

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Search Results for “9-point-circle”

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 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 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 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

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
And the envelope please...
What is the phantom curve you see when you look at a set of lines, perpendicular to a set of chords through a common point in a circle?

Tags: envelope, circle, ellipse, hyperbola

By Andrew Zhao
Euclids Elements – Book 3 – Proposition 08
This proposition proves that line AD is longest, ED is shorter, FD is shorter than ED, and CD is even shorter.and that for any line there is only one other line with a point on the circle and a point at D that is equal. (Unless you drag it to somewhere it's not supposed to be) I like it because it’s colorful.

Tags: Euclid, Elements, Geometry, Triangle

By Phil Todd
Pedal Triangles
The loci of the midpoints of the sides of pedal triangles form ellipses as the pedal point moves around a circle.    


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