For a better understanding of the solution/explanation provided here, please go through the diagram in the file that has been attached.
To solve this question we will use the following theorem: "An Angle formed by a chord and a tangent that intersect on a circle is half the measure of the intercepted arc
".
As can be seen from the diagram, the intercepted arc is BC and it's angle is [tex] \angle BOC=76^{\circ} [/tex].
Therefore, as per the theorem, [tex] m\angle BCP=\frac{1}{2}\times m\angle BOC [/tex]
[tex] \therefore m\angle BCP=\frac{1}{2}\times 76^{\circ}=38^{\circ} [/tex]
Thus the third option is the correct option.
