1. **Problem statement:** We have a circle with center O and a tangent line EDC touching the circle at point D. We need to find the size of angle $z$ formed between the tangent line and the chord inside the circle. 2. **Key fact:** The angle between a tangent and a chord through the point of contact equals the angle in the alternate segment of the circle. 3. **Given angles:** Angle at A is $12^\circ$, angle at D inside the circle is $38^\circ$, and angle $z$ is the angle between the tangent and chord at D. 4. **Using the alternate segment theorem:** Angle $z$ equals the angle in the alternate segment, which is the angle at A, $12^\circ$. 5. **Therefore,** $$ z = 12^\circ $$ 6. **Reason:** The tangent-chord angle theorem states that the angle between a tangent and a chord at the point of contact equals the angle subtended by the chord in the alternate segment of the circle. Final answer: $$ z = 12^\circ $$