Wingeom Angles & Arcs 2
Wingeom Angles & Arcs 2
Consider the diagram below. In the circle on the left you will find two secants intersecting a circle. Your assignment is to demonstrate that the measure of the angle of intersection is one-half the difference of the measures of the intercepted arcs. In the circle on the right you will find a tangent and a secant. Your assignment is to demonstrate that the measure of the angle of intersection, once again, is one-half the difference of the measures of the intercepted arcs.
Construct Circle Centered at A with Radius AB
Put the mouse in the Btn/Segment mode. Using the right mouse button, place point A and B on the screen. If you do not see the little circles that represent points, do Edit/labels/offset. On the command bar select Circle/Radius-center. In the pop-up frame, complete the information: centered at A, (●) circle through point B, draw and close.
Construct the Two Secants
With the mouse in the Btns/Segment mode, using the right mouse button, very carefully place points C, D, and E (not F and I!). Connect D to C (if you do C to D the order of further labels in this document will be changed) and C to E, in the usual manner.
Determining F and I
From the command bar, select Point/Intersection/Mixed. Fill in the information: line DC and highlight center A; through B; mark. Repeat this technique for CE and close.
Determine the Relationship between the Angle and the Intercepted Arcs
On the command bar select Meas. Type ................
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