Question

If the points A(4,3) and B(x,5) are on the circle with centre O(2,3), find the value of x.

Answer 1

Since A and B lie on the circle having centre O.

Therefore, OA = OB

$\sqrt{(4-2{)}^2+(3-3{)}^2}=\sqrt{(x-2{)}^2+(5-3{)}^2}$

$2=\sqrt{(x-2{)}^2+4}$

$(x-2{)}^2+4=4$

$(x-2{)}^2=0$

$x-2=0$

$x=2$