In the diagram, $X$ and $Y$ lie on the line $AB$ so that $BX = 9\text{ cm}$ and $AY = 11\text{ cm}$. Arc $BC$ is an arc of a circle with centre $X$ and radius $9\text{ cm}$, and $CX$ is perpendicular to $AB$. Arc $AC$ is an arc of a circle with centre $Y$ and radius $11\text{ cm}$.
(a)[1]
Show that angle $XYC$ is $0.9582$ radians, correct to $4$ significant figures.
(b)[6]
Find the total perimeter of $ABC$.
(c)[1]
The function $g$ is defined by $g(x) = 2x$ for $-a < x < a$, where $a$ is a constant. State the greatest possible value of $a$ for which $fg$ can be formed.
(d)[2]
Assuming that $fg$ can be formed, find an expression for $fg(x)$ and simplify it.
Worked solution & mark scheme
This 10-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Angle obtained using $\sin^{-1}\left(\frac{9}{11}\right)=0.9582$” …