In the given figure, the measure of the central angle CAD is 80°, the major arc is arc CBD, and minor arc is arc CD. The measure of arc BEC is 2.27r and that of arc BC is 0.87r.
About the Central Angle:
An angle formed by two radii of a circle is known as a central angle. Thus, arc BC and arc CD both subtends central angles at the center.
Since BD is the diameter of the circle,
∠BAC + CAD = 180°
It is given that ∠BAC = 100°
⇒ ∠CAD = 180° - 100°
⇒ ∠CAD = 80°
About Major Arc:
The arc which subtends an angle greater than 180° at the center, is called a major arc.
Angle subtended by arc BEC = 360° - m(arc CD)
= 360° - 80°
= 280° > 180°
∴ Arc BEC is the major arc
About Minor Arc:
The arc which subtends an angle less than 180° at the center, is called a minor arc.
⇒ Arc CD is the minor arc.
Calculating arc BEC and arc BC:
Let us assume the radius of the circle is r.
Then, the formula of the measure of an arc is given by,
θ × (π/180) × r
Here, θ is the angle ( in degrees) subtended by the arc at the center.
Arc BEC = 260 × (π/180)r ......... [Put π = 3.14]
= 2.27r
Similarly, arc BC = 100 ×(π/180) × r .......... [Put π = 3.14]
= 0.87r
Learn more about an arc here:
brainly.com/question/16930503
#SPJ1
