i just wana know proof of angle of intersection of two circlein cordinate geometry ..........interms of cosine angle

at first find the point of intersection of curves....let it be A..

 now make a tangent to the curve separately at this point ...

there will be 2 tangents with different slopes...let slope of tangents are

m₁,m_{2 respectively...}

then we have

                     tan@=m2-m1/1+m1m2

  @ is the angle bw tangents and it is called angle of intersection of two curves.....

   sec²@ =(1+tan² @)

     from here calculate cos@