Question:
In the diagram, is an arc of a circle, centre and radius , and angle . The point X lies on OB and AX is perpendicular OB.
(i) Show that the area, , of the shaded region is given by
(ii) In the case where and , find the perimeter of the shaded region , leaving your answer in terms of and .
Attempt:
(i) Area of shaded region = Area of sector of circle - Area of triangle
Area of sector of circle
Area of Triangle
Length
Length
Length
Breath
Breath
Breath
Area of Triangle
Area of Triangle
Area of shaded region = Area of sector of circle - Area of triangle
are my steps for showing the area of the shaded region correct?
(ii) Perimeter of Shaded Region = Arc lenght of circle AB + AX + XB
Arc length of circle
Arc length of circle
Length of AX
How can I get the length of in terms of ? I know that but if I used this would the vanish?