First, draw a diagram to visualize the situation:
Since BC is tangent to the circle P, then the angle C is a right angle.
Then, the triangle ACB is a right triangle. From the Pythagorean Theorem, we know that:
[tex]AB^2=AC^2+BC^2[/tex]
Since AB and BC are known, isolate the unknown AC from the equation:
[tex]\Rightarrow AC=\sqrt{AB^2-BC^2}[/tex]
Replace AB=12 and BC=5:
[tex]\Rightarrow AC=\sqrt{12^2-5^2}=\sqrt{144-25}=\sqrt{119}\approx10.9087[/tex]
Since P is the center of the circumference and A, C are points in the circumference, then AP=PC. This implies that AC=2AP. Then:
[tex]AP=\frac{1}{2}AC=\frac{1}{2}\sqrt{119}\approx5.5[/tex]
Therefore, the correct choice is option B) 5.5 units.
