A chock is a block placed against a wheel or rounded object, to prevent it from moving. Jenny had to come up with a prototype for the design of a new wheel chock. Jenny drew a model of the wheel chock and the cross section is shown below.

1. Find the radius $r$ using the result from part (a).

From part (a),
$BC=\sqrt{28(7+r)}.$
Given $BC=20$,
$20^2=28(7+r)$
$400=196+28r$
$28r=204$
$r=\frac{51}{7}.$

2. Find the shaded area by subtracting the sector area from triangle $OCB$.

Since $A$ lies on $OB$, $\angle AOC=\angle BOC=x$.

In right triangle $OCB$,
$\tan x=\frac{BC}{OC}=\frac{20}{51/7}=\frac{140}{51}.$
Hence
$x=\tan^{-1}\left(\frac{140}{51}\right).$

Area of shaded region
$=\text{area of }\triangle OCB-\text{area of sector }OAC$
$=\frac12\left(\frac{51}{7}\right)(20)-\frac12\left(\frac{51}{7}\right)^2\tan^{-1}\left(\frac{140}{51}\right)$
$=40.4\text{ cm}^2\quad\text{(3 s.f.)}.$

1. Identify the angle formed by $OC$ and $CB$.

Since $OC \perp CB$,
$\angle OCB = 90^\circ.$

2. Use the circle angle property to justify whether the points are concyclic.

An angle in a semicircle is a right angle. Conversely, if $\angle OCB = 90^\circ$, then $OB$ is the diameter of a circle passing through $C$.

Therefore, $O$, $B$ and $C$ lie on the circumference of a circle.