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The diagram provided appears to depict a circle with various geometric elements, including angles and lines associated with a triangle, a tangent, and chords. To break down the key components:

- \( O \) is the center of the circle.
- \( A \), \( B \), and \( C \) are points on the circle.
- \( D \), \( L \), and \( M \) seem to define a tangent to the circle, with \( LD \) likely being the tangent at point \( A \).
- The angle \( \angle BAC \) is labeled as \( 76^\circ \).
- Two other angles \( x \) and \( y \) are indicated in the diagram, likely involving points \( C \) and \( O \).

### Approach to solving:
We may be required to find angles \( x \) and \( y \) based on properties of the circle, such as:
- The angle subtended by a chord at the center vs. the angle subtended on the circumference.
- Properties of tangents (the angle between a tangent and a radius is 90 degrees).
- Relationships between angles in cyclic quadrilaterals, if relevant.

Before proceeding, could you clarify if you need to solve for \( x \) and \( y \), or if there are other specific questions related to this diagram?

Let me know if you want to proceed with solving for these angles, and I can walk through the process!

In the provided diagram, a circle is intersected by a tangent, with various angles including a 76° angle and two unknowns (x and y) inside the circle. Find the values of x and y based on geometric principles.

In this geometry problem, we solve for unknown angles x and y in a diagram involving a circle, a tangent, and a 76° given angle. Learn how to apply the Tangent-Secant Theorem and other circle properties.

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