Remark
The central angle and the arc measurement are equal so <APB = 60o
Every triangle has 180o. There are no exceptions to this rule.
The triangle is at least isosceles because two of it's sides are radii and each radii of a circle is equal to any other radius.
Equation and solution for the base angles.
2x + 60 = 180
2x = 180 - 60
2x = 120
x = 120/2
x = 60
Conclusion
That means that all three angles are 60 which means that all three sides are equal. Since AB is 12, AP is also 12
