# Search Results for “Angle”

##### 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.##### 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.##### 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.##### 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