In the given figure of circle :
AC is the diameter
AC = 46
Since, Diameter is the twice of radius. So,
Radius = Diameter/2
Radius = 46/2
Radius = 23
Area of Circle:
The area of circle is express as :
[tex]\text{ Area of Circle = }\Pi(radius)^2[/tex]Substitute the value of radius = 23
[tex]\begin{gathered} \text{ Area of Circle = }\Pi(radius)^2 \\ \text{ Area of Circle =}\Pi(23)^2 \\ \text{ Since }\Pi=3.14 \\ \text{Area of Circle =}3.14\times23\times23 \\ \text{Area of Circle =}1661.06 \end{gathered}[/tex]Area of Circle is 1661.06
Circumference of Circle :
The circumference of circle is express as :
[tex]\text{ Circumference of circle = 2}\Pi(radius)[/tex]Substitute the value of radius =23
[tex]\begin{gathered} \text{ Circumference of circle = 2}\Pi(radius) \\ \text{ Since }\Pi=3.14 \\ \text{Circumference of circle = 2}\times3.14\times23 \\ \text{Circumference of circle = }144.44 \end{gathered}[/tex]Circumference of circle is 144.44
Arce Length:
The expression for the arc length is
[tex]\text{ Arc Lenth = radius (Angle substended by the arc)}\frac{\Pi}{180}[/tex]Since Angle AEB and DEC are vertically opposite angle
Angle AEB = Angle DEC = 63
Substitute the value and simplify:
[tex]\begin{gathered} \text{ Arc Lenth = radius (Angle substended by the arc)}\frac{\Pi}{180} \\ \text{ Arc Length=23(63}^o)\frac{\Pi}{180} \\ \text{Arc length =}23\times1.099 \\ \text{Arc Length=}25.277 \end{gathered}[/tex]Arc Length = 25.277
Area of sector:
The expression for the area of sector is :
[tex]\text{ Area of sector =}\frac{\theta}{360}\times\Pi(radius)^2[/tex]Substitute the value
[tex]\begin{gathered} \text{ Area of sector =}\frac{\theta}{360}\times\Pi(radius)^2 \\ \text{ Area of sector =}\frac{63}{360}\times3.14(23)^2 \\ \text{ Area of sector}=0.175\times1661.06 \\ \text{ Area of sector = }290.68 \end{gathered}[/tex]Area of Sector DEC is 290.68
