a. Central angle: Angle BAC
b. A major arc is: Arc BEC
c. A minor arc is: Arc BC
d. Measure of arc BEC in circle A = 260°
e. Measure of arc BC = 100°
What is the Central Angle Theorem?
According to the central angle theorem the measure of central angle (i.e. angle BAC in circle A) is the same as the measure of the intercepted arc (i.e. arc BC in circle A).
What is a Central Angle?
Referring to the image given, a central angle (i.e. angle BAC) is formed by two radii of a circle (i.e. AB and AC in circle A), where the vertex of the angle (i.e. vertex A in circle A) is at the center of the circle.
What is a Major Arc?
An arc that is bigger than a semicircle (half a circle) or with a measure greater than 180 degrees is called a major arc of a circle.
What is a Minor Arc?
An arc that is smaller than a semicircle (half a circle) or with a measure less than 180 degrees is called a minor arc of a circle.
a. Central angle in circle A is: ∠BAC
b. Major arc in circle A is: Arc BEC
c. Minor arc in circle A is: Arc BC.
d. Based on the central angle theorem, we have:
Measure of arc BEC in circle A = 360 - 100
Measure of arc BEC in circle A = 260°
e. m∠BAC = 100° [given]
Based on the central angle theorem, we have:
m(arc BC) = m∠BAC
Measure of arc BC = 100°
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