# Search Results for “Triangle”

By Duncan
##### Similar Triangle Incenter
This problem showed up in a math competition. See what you can make of it.

Tags: incenter, circle, similar-triangles

##### 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

##### Morley's Theorem
An Illustration of Morley's Theorem

Tags: Triangle, angle-trisector, Morley's-theorem, equilateral

##### 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

##### Ellipse Incenter Locus
What is the locus of the incenter of the triangle formed by the string in the "two pins and a piece of string" construction of an ellipse?

Tags: ellipse, locus

##### cosine rule test
Find the third side of the triangle.  Can you do it without resorting to trial and error? Refresh the page to get a new example.

Tags: cosine-rule, trigonometry

##### 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

##### Simple Similar Triangles
Drag points A, B, and C to change the size and shape of the blue triangle, and its white counterpart that is similar (constrained by proportional SAS). Drag the Red point D to change the ratio in sizes. Observe the multitude of calculated output lengths and angles, and how they match the proportion value, proving similarity, regardless of the triangles' shapes/sizes.

Tags: Triangles, Similar, Ratios, Draggable, Outputs,

##### Parabola Property
The triangle containing the normal and tangent at a point on a parabola sits inside a semicircle centered at the parabola's focus.

Tags:

##### Parabola Tangent Circumcircle
3 tangents of a parabola form a triangle.  Its circumcircle passes through the parabola's focus.

Tags: parabola, focus, circumcircle