Matematicas Visuales | Central and inscribed angles in a circle | Mostration

The general case of the Central Angle Theorem can be proved using the previous case. To do that we can draw the diameter that pases through the vertex of the inscribed angle. Then, depending on the position of the points, it is enough to add or to subtract some angles.

In this position we have to add two central angles (and we use Case II):

Central Angle Theorem General Case: adding two angles | matematicasvisuales

In this position we have to substract two central angles (and we use Case II):

Central Angle Theorem General Case: substracting two angles | matematicasvisuales

With Case I, Case II and this General Case we have finished the demostration of the Central Angle Theorem.

Central Angle Theorem. End of demostration of the Central Angle Theorem| matematicasvisuales

REFERENCES

Euclides, The Elements

LINKS

Central and inscribed angles in a circle
Central angle in a circle is twice the angle inscribed in the circle.

Central and inscribed angles in a circle | Mostration | Case I
Interactive 'Mostation' of the property of central and inscribed angles in a circle. Case I: When the arc is half a circle the inscribed angle is a right angle.

Central and inscribed angles in a circle | Mostration | Case II
Interactive 'Mostation' of the property of central and inscribed angles in a circle. Case II: When one chord that forms the inscribed angle is a diameter.