Central and Inscribed Angle in a Circle: Case II


CASE 2. When the vertex is one of the ends of the diameter and the cord draws up from the other end, the angle in center is the double of the angle in the vertex. In this case we want to prove that We draw the line OP parallel to AB, and then Adding this two angles we get the result: Now is very easy to probe the general case. You can see an interactive demostration of the Central and inscribed angles in a circle  General Case. REFERENCES
Euclides, The Elements
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Using a ruler and a compass we can draw fifteen degrees angles. These are basic examples of the central and inscribed in a circle angles property.
You can draw a regular pentagon given one of its sides constructing the golden ratio with ruler and compass.
In his book 'Underweysung der Messung' Durer draw a nonregular pentagon with ruler and a fixed compass. It is a simple construction and a very good approximation of a regular pentagon.
