You are a helpful assistant that can solve the given question step by step with the help of the wikipedia search tool and python interpreter tool. Given a question, you need to first think about the reasoning process in the mind and then provide the answer. During thinking, you can invoke the wikipedia search tool to search and python interpreter tool to calculate the math problem for fact information about specific topics if needed. The reasoning process and answer are enclosed within <think> </think> and <answer> </answer> tags respectively, and the search query and result are enclosed within <search> </search> and <result> </result> tags respectively. For example, <think> This is the reasoning process. </think> <search> search query here </search> <result> search result here </result> <think> This is the reasoning process. </think> <python> python code here </python> <result> python interpreter result here </result> <think> This is the reasoning process. </think> <answer> The final answer is \[ oxed{answer here} \] </answer>. In the last part of the answer, the final exact answer is enclosed within oxed{} with latex format.
system
In the rectangular coordinate system xOy, the parametric equation of curve C1 is given by $$\begin{cases} x=5cos\alpha \\ y=5+5sin\alpha \end{cases}$$ (where α is the parameter). Point M is a moving point on curve C1. When the line segment OM is rotated counterclockwise by 90° around point O, line segment ON is obtained, and the trajectory of point N is curve C2. Establish a polar coordinate system with the coordinate origin O as the pole and the positive half of the x-axis as the polar axis.

1. Find the polar equations of curves C1 and C2.
2. Under the conditions of (1), if the ray $$θ= \frac {π}{3}(ρ≥0)$$ intersects curves C1 and C2 at points A and B respectively (excluding the pole), and there is a fixed point T(4, 0), find the area of ΔTAB.
user
15-5 \sqrt {3}
rule
In the rectangular coordinate system xOy, the parametric equation of curve C1 is given by $$\begin{cases} x=5cos\alpha \\ y=5+5sin\alpha \end{cases}$$ (where α is the parameter). Point M is a moving point on curve C1. When the line segment OM is rotated counterclockwise by 90° around point O, line segment ON is obtained, and the trajectory of point N is curve C2. Establish a polar coordinate system with the coordinate origin O as the pole and the positive half of the x-axis as the polar axis.

1. Find the polar equations of curves C1 and C2.
2. Under the conditions of (1), if the ray $$θ= \frac {π}{3}(ρ≥0)$$ intersects curves C1 and C2 at points A and B respectively (excluding the pole), and there is a fixed point T(4, 0), find the area of ΔTAB.
train