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

★GIVEN★

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

★To Find★

The value of x.

★SOLUTION★

It is said O(2,3) is the centre of the circle.

• x = 2
• y = 3

By using mid-point formula,

$\large{\green{\underline{\boxed{\bf{For\:x=\dfrac{x_{1}+x_{2}}{2}}}}}}$

$\large{\green{\underline{\boxed{\bf{For\:y=\dfrac{y_{1}+y_{2}}{2}}}}}}$

• $\large{\sf{Let\:4,x\:be\:x_{1},x_{2}\:respectively.}}$
• $\large{\sf{Let\:3,5\:be\:y_{1},y_{2}\:respectively.}}$

Now,

$\large\implies{\sf{For\:x=\dfrac{x_{1}+x_{2}}{2}}}$

$\large\implies{\sf{2=\dfrac{4+x}{2}}}$

$\large\implies{\sf{2\times2=4+x}}$

$\large\implies{\sf{4-4=x}}$

$\large\therefore\boxed{\bf{x=0.}}$

★VERIFICATION★

$\large\implies{\sf{For\:x=\dfrac{x_{1}+x_{2}}{2}}}$

$\large\implies{\sf{2=\dfrac{4+0}{2}}}$

$\large\implies{\sf{2=\dfrac{4}{2}}}$

$\large\implies{\sf{2=\dfrac{\cancel{4}}{\cancel{2}}}}$

$\large\implies{\sf{2=2}}$

$\large\therefore\boxed{\bf{LHS=RHS.}}$

So, B is (0, 5).

Value of x = 0.