EDSC 121 - Basic Parts of a Circle (MATH10MG-IIIg-h-11-13)

Autore:Christian Cire B. Sanchez (Kris Chan)

Figure 1: Basic Parts of a Circle

Recalling of Concepts

In your previous years in Mathematics, Circles have been defined as two-dimensional plane figures made up of a curved line. It is round, and all points on the curved line are an equal distance from its center. We learned that the curved line is called the Circumference. It is the distance around the circle, or basically, its Perimeter. It is denoted by the symbol C, and the formula for the Circumference is indicated below:

and

We have also established that the Circle's diameter is twice the measure of its radius.

Which is Which?

1. Analyze Figure 1. From the given set of lines, angles, and points, identify which part of the circle is described. Answer in ALL CAPS (ex., POINT, LINE SEGMENT, RAY) I. Line CD II. Line AB III. Line EAF IV. Arc EDF V. Arc ECD VI. Line IH VII. Line GK VIII. Arc EFI IX. Angle FAB X. Angle DJC

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Figure 2: Angles and their Intercepted Arc

Relationships of the Angles and their Intercepted Arc

Analyze Figure 2. In the first breakpoint, we can see Circle A with its two points, Points B and C. Following the sequence, a new angle was formed by the two radii, namely Angle CAB. In the third breakpoint, Point Dwas introduced. The next sequence creates two chords, Chords BD and CD, and together, they form Angle CDB. The fifth breakpoint introduces Point E, and the last breakpoint also creates two more chords, Chords BE and CE, forming Angle CEB. 2. Angle CAB is located in the Center, which is Point A. While Angle CDB and Angle CEB are located in the Circumference. From the choices below, identify which is the reasonable name for them and their respective theorems.

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A
Central Angle Theorem (Angle CAB) and Inscribed Angle Theorem (Angles CDB and CEB)
B
Adjacent Angle (Angle CAB) and Vertical Angle Theorem (Angles CDB and CEB)

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Manipulate the applet by moving Points C, B, D, and E. As the measurements change, find a relationship between the angles and their intercepted arc. For the measure of Arc CB to appear, click the next button. 3. Arc CB is intercepted by Angle CAB, Angle CEB, and Angle CDB. Try dividing: I. Angle CAB divided by Angle CEB or Angle CDB II. Arc CB divided by Angle CEB or Angle CDB III. Arc CB divided by Angle CAB IV. Angle CEB or Angle CDB divided by Angle CAB Identify which option shows the correct congruence and relationship between angles and arcs, establishing that they intercept (subtend) the same arc, which is Arc CB.