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Search Results for “Angle”

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 Phil Todd
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.

Tags: Archimedes, circle, angle

By Phil Todd
Maximum Angle of Reflection
Drag B to find the maximum angle of reflection. The circumcircle of ABC is the locus of all points which subtend the same angle on chord AC. In general G is inside the circumcircle and so angle AGC < angle ABC. The exception is when B=G.

Tags: caustic, reflection

By Phil Todd
Protractor
Practice using a protractor. Drag the blue points to give yourself a new angle to work on.  Line up the red points to use the protractor. Press the Angle button to show and hide the answer

Tags: protractor, angle

By Phil Todd
Euclid Book 6 Proposition 15
In equal triangles which have one angle equal to one angle the sides about the angle are reciprocally proportional; and those triangles which have one angle equal to one angle, and in which the sides about the equal angle are reciprocally proportional are equal.

Tags: Euclid

By Andrew Zhao
Euclids Elements - Book 1 - Proposition 45
Creating a parallelogram equal to a given quadrilateral with a given angle.

Tags: Euclid, Elements, Geometry, Parallelogram, Triangle, Angle

By Phil Todd
Regiomontanus Problem
We seek the place on the earth's surface where a vertically suspended bar (or the rings of Saturn) look the biggest. A machine to solve this problem consists of a mass fixed to the earth's surface and a couple of bars attached to the mass and constrained to pass through the ends of the bar.  A spring between the bars pushes them apart. The machine reaches equilibrium when the bars are as far apart as possible, hence finding the solution to Regiomontanus' Problem. You can drag the ends of the bar to change the problem. Press Show to see the circumcircle of the ends of the bar and the mass.  You should notice something about the position of this circumcircle at equilibrium. Can you explain what you have noticed?

Tags: Regiomontanus, circle, angle

By Phil Todd
Morley's Theorem
An Illustration of Morley's Theorem

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

By Phil Todd
Ferry Problem
A ferry with speed v is crossing a river whose current is w.  Try different combinations of v and w.  Drag the red point to alter the ferry angle.  Press the Play button to see the result. Press Stop to reset the simulation. For what values of v and w is the ferry able to cross the river without any downstream drift? As w increases relative to v, how does the ferry angle change? If the river current increases, the ferry eventually has to accept some downstream drift.  For such cases try to find the ferry angle which gives the least drift. As the current increases further what happens to this "minimum drift angle"?

Tags: vector, calculus, triangle, ferry

By Phil Todd
Optimal Performance of Box Solar Cooker
The solar concentration ratio of a solar cooker is the ratio of the amount of sunlight concentrated on the target to the size of the target. This model presents the best situation for a given lid angle, and lets you see how much light can be captured at that lid angle. The question is:  what lid angle captures the most sunlight?

Tags: solar-cooker, reflection


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