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?