Search Results for “Theorem”
Pythagorean Theorem Calculator
A simple Pythagorean Theorem calculator that accepts inputs for either two sides or one side and the hypotenuse, then calculates the remaining side using the Pythagorean Theorem. Both exact and approximate solutions are provided, as well as the complete Pythagorean Theorem version.
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.
Cyclic Quadrilateral Theorem
The Cyclic Quadrilateral Theorem states that for a quadrilateral inscribed in a circle, the measures of opposite angles must add to 180 degrees. Drag the points and observe the angle measures to see how this theorem holds true.
A Median Theorem
D is the midpoint of AC and E the midpoint of BD. What can you say about the position of F?
A geometry theorem
H1,H2 and H3 are feet of altitudes, M1,M2,M3 are midpoints. H is the orthocenter. X2,X3,Y1,Y3,Z1,Z2 are formed by reflecting H1,H2 and H3 in the other altitudes. X,Y,Z are the intersections between the lines joining midpoints to these reflected points. Observe that H appears to be the incenter of XYZ so long as ABC is acute angled. Otherwise it appears to be one of the excenters
An Arbelos Theorem
The large circle in the diagram has radius 1. Circles centered at A and B are tangent and each tangent to the large circle. (The shape in between the circles is called an arbelos after the Greek for a cobbler's knife, which it apparently resembles.) BC is tangent to circle A and AD tangent to circle B. EF and GH are perpendicular to AB. Can you show that they are equal? Can you find an expression for their length in terms of the radius of circle A? Are they the same size as Archimedes "twins"
Archimedes Angle Theorem
A is the circle center, and |AB| = |BD|. What is the relationship between angle CAE and angle BDA? You can drag B and C and watch it change. Can you prove the relationship? This is an example from Archimedes Book of Lemmas.
