The line Ax+By+=0 cuts the circle by `x^2+y^2+Ax+By+C=0`at P and Q. The line A'x +B'x+C'=0 cuts the circle `x^2+y^2+a'x+b'y+c'=0` at R and S.If P,Q, R and S are concyclic then show that `det (( a-a", b-b',c-c'),(A,B,C),(A',B',C'))=0`

The line A x+B y+C=0 cuts the circle x^2+y^2+a x+b y+c=0 at Pa n dQ . The line A^(prime)x+B^(prime)x+C^(prime)=0 cuts the circle x^2+y^2+a^(prime)x+b^(prime)y+c^(prime)=0 at Ra n dSdot If P ,Q ,R , and S are concyclic, then show that |a-a ' b-b ' c-c ' A B C A ' B ' C '|=0

The line A x+B y+C=0 cuts the circle x^2+y^2+a x+b y+c=0 at Pa n dQ . The line A^(prime)x+B^(prime)x+C^(prime)=0 cuts the circle x^2+y^2+a^(prime)x+b^(prime)y+c^(prime)=0 at Ra n dSdot If P ,Q ,R , and S are concyclic, then show that |a-a ' b-b ' c-c ' A B C A ' B ' C '|=0

The line A x+B y+C=0 cuts the circle x^2+y^2+a x+b y+c=0 at Pa n dQ . The line A^(prime)x+B^(prime)x+C^(prime)=0 cuts the circle x^2+y^2+a^(prime)x+b^(prime)y+c^(prime)=0 at Ra n dSdot If P ,Q ,R , and S are concyclic, then show that |a-a ' b-b ' c-c ' A B C A ' B ' C '|=0

The line ax +by+c=0 is an normal to the circle x^(2)+y^(2)=r^(2) . The portion of the line ax +by +c=0 intercepted by this circle is of length

The line ax +by+c=0 is an normal to the circle x^(2)+y^(2)=r^(2) . The portion of the line ax +by +c=0 intercepted by this circle is of length

The line ax +by+c=0 is an normal to the circle x^(2)+y^(2)=r^(2) . The portion of the line ax +by +c=0 intercepted by this circle is of length

Show that the circles x^2 +y^2 + 2ax + c = 0 and x^2 + y^2 + 2by + c = 0 touch each other if 1//a^2 + 1//b^2 = 1//c.

Prove that the line ax + by + c = 0 will be a tangent to the circle x^2+y^2=r^2 if r^2(a^2+b^2)=c^2 .