Is the hypotenuse always the radius and adjacent side is the distance

You're asking a great clarifying question about the setup of these right-angled triangles!

Yes, in the context of a right-angled triangle formed by the radius, the distance from the center to a chord, and half the chord length:

• The hypotenuse is always the radius ($r$). This is because the radius connects the center to a point on the circle (an endpoint of the chord), and it is the longest side, opposite the $90^\circ$ angle.
• The terms "adjacent side" and "opposite side" depend on which acute angle you are referring to in the triangle.
  • If you are considering the angle at the center of the circle (half of the angle subtended by the chord), then the adjacent side to this angle is the distance from the center to the chord ($d$).
  • If you are considering the angle at the endpoint of the chord (between the radius and the chord), then the adjacent side to this angle would be half the chord length.

So, for the common scenario where we use the angle at the center, your statement is correct: the hypotenuse is the radius, and the adjacent side (to the central angle) is the distance from the center to the chord.