Answer:
Step-by-step explanation:
1). Since, XM is the radius of the circle,
Therefore, area of the circle = [tex]\pi r^{2}[/tex]
= [tex]\pi (XM)^2[/tex]
= [tex]\pi (12)^2[/tex]
= 452.39 units²
2). Circumference of a circle = 2πr
= 2π(XM)
= 2π(12)
= 24π
= 75.40 units
3). By applying Pythagoras theorem in ΔYXM,
YM² = XY² + XM²
(43)²= (XY)² + (12)²
1849 - 144 = (XY)²
XY = 41.29 units
4). tan(∠M) = [tex]\frac{\text{Opposite side}}{\text{Adjacent side}}[/tex]
= [tex]\frac{XY}{XM}[/tex]
m∠M = [tex]tan^{-1}(\frac{41.29}{12} )[/tex]
= 73.79°
5). Area of ΔXYM = [tex]\frac{1}{2}(\text{Base)}(\text{Height})[/tex]
= [tex]\frac{1}{2}(41.29)(12)[/tex]
= 247.74 square units
6). Area of the minor sector created by ΔXYM = [tex]\frac{\theta}{360}(\pi r^2)[/tex]
= [tex]\frac{73.79}{360}(452.39)[/tex]
= 92.73 units²
