The exercise you uploaded appears to involve geometric and algebraic reasoning, particularly with circles, tangents, and line segments. Here's a breakdown of the tasks:

1. You are given the following information:

   • $A$, $B$, and $M$ are points on the circle.
   • The circle’s center is denoted by $O$.
   • There is a line segment $AB$, with $AB = 3 \sqrt{2}$.

2. The tasks involve proving geometric relationships using the properties of circles, tangents, and perpendicularity.

Breakdown of Questions:

• a) “Prove that (AB) ⊥ (EF)”: This suggests proving that the line segment $AB$ is perpendicular to the line $EF$. It could involve using the fact that tangents at a point of a circle are perpendicular to the radius of the circle at that point.

• b) Determine the center of the circle, the radius, and further prove that certain points are on a circle: This is a geometric proof where you'll need to calculate the radius and verify the locations of certain points based on the geometric setup.

• c) Proving the perpendicularity of segments involving tangents and lines related to a circle.

Approach for Solving:

1. Using properties of tangents and perpendicularity: In this part of the task, since $AB$ is a chord of the circle and you are trying to prove that it is perpendicular to another line $EF$, we may need to apply the fact that the radius of a circle is perpendicular to a tangent at the point of tangency.

2. Circle equation and geometric construction: For part b, you'd want to determine the coordinates of the center of the circle and the radius, then verify if the points given satisfy the geometric conditions (like being on the circle).

Do you want me to work through these steps in detail for you?