1. **Determine the angle $\theta$ at which the tangent line is drawn.** Given the tangent line at point A and chord AB, the angle between the tangent and chord equals the measure of the inscribed arc opposite the chord. **Formula:** $$\theta = \text{measure of the intercepted arc}\n$$ From the figure, if the arc opposite the chord is 53.13°, then $\theta = 53.13^\circ$. **Answer:** A. 53.13° 2. **Find the measure of the minor arc AB given the major arc AB is 286°.** The total circle is 360°, so: $$\text{minor arc} = 360^\circ - 286^\circ = 74^\circ$$ **Answer:** A. 74° 3. **Find the length of the chord subtending a 40° angle at the center with radius 7 cm.** **Formula for chord length:** $$c = 2r \sin\left(\frac{\theta}{2}\right)$$ Calculate: $$c = 2 \times 7 \times \sin\left(\frac{40^\circ}{2}\right) = 14 \times \sin(20^\circ)$$ Using $\sin(20^\circ) \approx 0.3420$: $$c \approx 14 \times 0.3420 = 4.788$$ **Answer:** A. 4.78 cm 4. **Largest isosceles triangle inscribed in a circle has a central angle of:** The largest isosceles triangle is equilateral, so each central angle is: $$\frac{360^\circ}{3} = 120^\circ$$ **Answer:** B. 120° 5. **Find the circumference of a circle with diameter 18 cm.** **Formula:** $$C = \pi d$$ Calculate: $$C = \pi \times 18 \approx 3.1416 \times 18 = 56.5487$$ **Answer:** B. 56.52 cm 6. **Find angle $x$ if intercepted arc measures 148°.** The angle formed by the intercepted arc at the circumference is half the arc: $$x = \frac{148^\circ}{2} = 74^\circ$$ **Answer:** A. 74° 7. **Radius perpendicular to tangent line at point of tangency forms what angle?** By definition, radius is perpendicular to tangent at point of tangency: $$\text{angle} = 90^\circ$$ **Answer:** A. 90° 8. **Angle subtended by a diameter at the circumference is:** By Thales' theorem, angle subtended by diameter is a right angle: $$90^\circ$$ **Answer:** B. 90°