It looks like you've provided a set of geometry questions involving circles, chords, diameters, and triangles inscribed in circles. Let's break down and analyze each problem:

1. Diagram with Diameter AB and Chord CD Intersecting at E:

• Given: AB is the diameter of circle $O$ and chord $CD$ intersects the diameter at point $E$.
• To Solve:
  • Since $AB$ is the diameter, by the Thales' theorem, $\angle CEB = 90^\circ$ if $C$ and $D$ lie on the circumference.
  • You can use properties of the circle and similar triangles to find specific lengths, angles, or other required elements.

2. Triangle ABC Inscribed in Circle P:

• Given: $\Delta ABC$ is inscribed in circle $P$ with distances from the center $P$ to each side of the triangle provided.
• To Solve:
  • The length of the radius $r$ of the circle can be determined if any of the distances or the circumradius formula is given.
  • The length of $AB$ and $AC$ might require knowing the triangle’s circumradius $R$ and applying the Law of Sines or another relevant formula.

3. Circle with Diameter QT Passing Through Point S:

• Given: $QT$ is a diameter passing through point $S$.
• To Solve:
  • The measure of $OP$ can be found if $O$ is the center of the circle and $P$ is some point on the circle or inside.
  • The length of $QR$ and $QT$ depends on the circle's properties and whether $QR$ is a chord, radius, or another element.

To move forward:

1. What is the radius of the circle in Problem 2?
2. What are the distances provided from the center $P$ to each side of the triangle in Problem 2?
3. Are there any specific lengths or angles given in Problems 1 and 3?
4. Can you upload a diagram for more precise analysis?
5. What is the position of point $S$ relative to the center in Problem 3?

Tip: Remember, when dealing with inscribed angles and chords in a circle, key theorems like the Inscribed Angle Theorem and properties of cyclic quadrilaterals are often useful.

Feel free to provide more details or upload a diagram for further assistance!