As shown in the figure, the point P is a moving point on the circle, the chord AB = 3, PC is the bisector of ∠ APB, ∠ BAC = 30 °. Q: when ∠ PAC is equal to what degree, the quadrilateral PACB has the largest area? What is the maximum area?

As shown in the figure, the point P is a moving point on the circle, the chord AB = 3, PC is the bisector of ∠ APB, ∠ BAC = 30 °. Q: when ∠ PAC is equal to what degree, the quadrilateral PACB has the largest area? What is the maximum area?

When point P is the midpoint of the superior arc AB, the area of △ PAB is the largest, then the quadrilateral PACB has the largest area. At this time, PC is the diameter of ⊙ o, PA = AB = 3, while ⊙ APC = 30 °, AC = 33pa = 1, ⊙ s △ PAC = 12 × 1 × 3 = 32, and the largest area of quadrilateral PACB is 2S Δ PAC = 3, that is, when ∠ PAC is equal to 90 degrees, the quadrilateral PACB has the largest area, and the largest area is 3