1. The problem is to understand and apply the circle theorem. 2. One common circle theorem states: "The angle subtended by a diameter at the circumference is a right angle." 3. This means if you have a triangle inscribed in a circle where one side is the diameter, the angle opposite that side is $90^\circ$. 4. Formula: If $AB$ is the diameter and $C$ is any point on the circle, then $\angle ACB = 90^\circ$. 5. Explanation: This happens because the triangle formed is a right triangle by the Thales' theorem. 6. Example: Suppose the diameter $AB$ is fixed, and point $C$ lies anywhere on the circle. Then $\angle ACB$ is always $90^\circ$. 7. This theorem helps in solving many geometry problems involving circles and right angles. 8. Summary: The key takeaway is that any triangle inscribed in a circle with one side as the diameter is a right triangle with the right angle opposite the diameter.