Circle and straight line x-2y+4? =? 0 is tangent to a (2,? 3),? The center of the circle is at point A, which is equal to x-2y+4? =? 0 on the vertical straight line (m).

x-2y+4？ =? 0，y？ =? x/2？ The slope of +4 is 1/2. The slope of l is -2 and the equation is y-3. =? -2(x-2)，？ y？ =? 7-2 times

The straight line x-y+ 1? =? 0，y？ =? X+ 1 (slope 1) also exceeds a (2,3). Let the other intersection with circle C be B(b,? b+ 1)

BC=？ (b-2)+(b+ 1-3)=？ 2(b-2)=(2√2)=？ eight

(b-2)=？ four

b？ =? 0 or b=4

( 1)? b？ =? 0,? B(0，？ 1)

The midpoint of AB is M( 1,? 2),? Exceeds m and is in line x-y+ 1? =? 0 The slope of the vertical straight line (n) is-1.

The equation of n is:? y-2？ =? -(x- 1)，？ y？ =? 3-x

The center C(4,-1) can be obtained by simultaneous equations of straight lines m and n.

Let the radius be r,? r=？ CA=？ 20

Equation of circle c:? (x-4)+？ (y？ +? 1)=? 20

(2)? b？ =? 4,? B(4，？ 5)

The midpoint of AB is M(3,? 4),? Exceeds m and is in line x-y+ 1? =? 0 The slope of the vertical straight line (o) is-1.

The equation of o is:? y-4？ =? -(x-3)，？ y？ =? 7-x

Simultaneous equations of straight lines m and o can get the center of the circle C(0,? 7)

Let the radius be r,? r=？ CA=？ 20

Equation of circle c:? x+？ (y？ -? 1)=? 20