a. Central angle in the circle is: Angle BAC
b. A major arc is: Arc BEC
c. A minor arc is: Arc BC
d. m(arc BEC) = 260°.
e. m(arc BC) = 100°.
What is the Central Angle Theorem?
The central angle theorem states that: the central angle measure of a circle equals the measure of the intercepted arc.
What is a Central Angle?
A central angle is formed by two radii of a circle, and the vertex of the angle is at the center of the circle.
What is a Major Arc?
Any arc that is more than half a circle (semicircle) or has a measure that is greater than 180 degrees, is referred to as a major arc of that circle. The measure of the major arc > 180 degrees.
What is a Minor Arc?
Any arc that is not more than half a circle (semicircle) or has a measure that is less than 180 degrees, is referred to as a minor arc of that circle. The measure of the minor arc < 180 degrees.
a. One central angle that can be identified in circle A is: Angle BAC
b. A major arc that can be identified in circle A is: Arc BEC
c. A minor arc that can be identified in circle A is: Arc BC.
d. According to the central angle theorem, we have:
m(arc BEC) = 360 - 100
m(arc BEC) = 260°
e. We are given that m(angle BAC) = 100°, therefore, according to the central angle theorem, we have:
m(arc BC) = m(angle BAC )
m(arc BC) = 100°
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