The Geometry of a Circle - By: Dennis Kapatos
The Geometry of a Circle - By: Dennis Kapatos
The Geometry of a Circle - By: Dennis Kapatos
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Words in () are what the students should be<br />
guided to conjecture. <strong>The</strong>y should not be told<br />
to them.<br />
Teacher’s Instructions<br />
Instructions (say aloud):<br />
Construct a circle AB<br />
Hide point B<br />
Construct Segments CD and ED as shown<br />
Questions:<br />
<strong>The</strong>se are a new type <strong>of</strong> line we haven’t seen<br />
yet. <strong>The</strong>y’re called secants. How might we define them?<br />
m CE on AB = 60.00 °<br />
Instructions:<br />
Construct the intersections, F and G, <strong>of</strong> these<br />
secants<br />
Measure arc angles CE and FG<br />
Measure angle D<br />
Move points C and/or E so that the measure <strong>of</strong> arc angle CE is a round number, say 60<br />
degrees<br />
Questions:<br />
As you move point D onto the circle, how does this situation look familiar? (It is the<br />
inscribed angle theorem from last class.) What about when D is inside the circle? Outside? Lets<br />
explore the relationships between these angles.<br />
Instructions:<br />
Select the measurement <strong>of</strong> angle D then the arc angle <strong>of</strong> FG<br />
From the graph menu, choose “plot as (x,y)<br />
Position your axis and change your unit values to make the graph fit nicely as shown<br />
<strong>The</strong> point that was created by the “plot as (x,y)” above, choose it and from the display<br />
menu, choose trace point<br />
Move point D around outside the circle<br />
C<br />
E<br />
A<br />
m FG on AB = 29.02 °<br />
F<br />
G<br />
D<br />
m! C D E = 1 5 . 4 9 °
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