A major sector \(LOM\) of a circle, with centre \(O\) and radius \(r cm\), has \(\angle LOM= \theta\) radians, as shown in the diagram. The perimeter of the sector is \(P cm\) and the area of the sector is \(A cm^2\).
(a) Write down, in terms of \(r\) and \(\theta\), expressions for \(P\) and \(A\).
\(P =r\theta+\)\(r\)
\(A =\) \(r^2\theta \)
Correct
Incorrect
Question 2 of 3
2. Question
3 point(s)
Given that \(r= {2}\sqrt{2}\) and that \(P=A\),
(b) Show that \(\theta=\frac{2}{{\sqrt{2}-1}}\). Were you able to show this?
Correct
Incorrect
Question 3 of 3
3. Question
2 point(s)
(c) Express \(\theta\) in the form \(a+b\sqrt{2}\), where \(a\) and \(b\) are integers to be found.