Question

In the circle, mBC=76degrees. The diagram is not drawn to scale. What is m angle BCP?

Answer 1

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
`\angle BOC=76^(\circ)`.

Therefore, as per the theorem,
`m\angle BCP=(1)/(2)* m\angle BOC`

`\therefore m\angle BCP=(1)/(2)* 76^(\circ)=38^(\circ)`

Thus the third option is the correct option.