IB Math HL Trigonometry Test 6 2018 P2 Q4

From point \(A\), lines \(AB\) and \(AC\) are tangent to a circle with centre \(O\) and radius \(r\) at \(B\) and \(C\). Let \(\angle BOC=\theta\).

1. Show that the area of quadrilateral \(ABOC\) is \(r^2\tan\frac{\theta}{2}\).[3]
2. The shaded region has the same area as sector \(OBDC\). Find \(\theta\) in degrees.[4]