Question

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

Answer 1

Given two points $A(4,3)$ and $B(x,5)$ on the circle with centre $O(2,3)$.

$OA$ and $OB$ are radii of the circle. Therefore, $OA=OB$.

Using Distance formula,

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

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

Since, $OA=OB$

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

$⟹\sqrt{4}=\sqrt{(x-2{)}^2+4}$

Squaring both sides, we get

$⟹4=(x-2{)}^2+4$

$⟹(x-2{)}^2=0$

$⟹x-2=0$

$⟹x=2$