1. **Problem Statement:** Show that if a chord subtends a 90° angle at a point on the circle, then the chord is a diameter. 2. **Key Concept:** The angle subtended by a chord at any point on the circle is related to the arc it intercepts. 3. **Formula and Theorem:** The angle subtended by a chord at the center of the circle is twice the angle subtended at any point on the circumference on the same side of the chord. 4. **Given:** Angle subtended by chord at point on circle = 90°. 5. **Using the theorem:** Let the chord subtend an angle $\theta$ at the center. Then $\theta = 2 \times 90° = 180°$. 6. **Interpretation:** An angle of 180° at the center means the chord passes through the center of the circle. 7. **Conclusion:** A chord passing through the center of the circle is a diameter. Therefore, if a chord subtends a 90° angle at a point on the circle, it must be a diameter.