Sides AB and AC in an equilateral triangle ABC with side length 3 is extended to form two rays emanating from the point A as shown in the figure. A point P is chosen outside the triangle ABC and between the two rays such that ∠ABP+∠BCP=180∘. If the maximum length of CP is M, then the value of M22 is

Sides AB and AC in an equilateral triangle ABC with side length 3 is e

1.	Sides AB and AC in an equilateral triangle ABC with side length 3 is extended to form two rays emanating from the point A as shown in the figure. A point P is chosen outside the triangle ABC and between the two rays such that ∠ABP+∠BCP=180∘. If the maximum length of CP is M, then the value of M22 is
Answer» Sides $A B$ and $A C$ in an equilateral triangle $A B C$ with side length $3$ is extended to form two rays emanating from the point $A$ as shown in the figure. A point $P$ is chosen outside the triangle $A B C$ and between the two rays such that $∠ A B P + ∠ B C P = 180^{\circ} .$ If the maximum length of $C P$ is $M,$ then the value of $\frac{M^{2}}{2}$ is