Plz i need to show work i don’t understand it’s

So, first, we should know that the length of OA is 7. Why? It's because OA is a radius and all radius in a specific circle are the same.

Next, we know that length AP is perpendicular to OA. How do we know this? It is because it is stated that AP is a tangent of OA. All tangents are perpendicular.

Knowing this, we could know that it is a right triangle, with lengths  7 and 25 as the legs and hypotenuse

Using Pythagorean theorem, 25^2 = 7^2 + b^2 

625 = 49 + b^2

576 = b^2

b = 24

So the length of AP is 24, or answer choice d.