Question

if A(2,0) and B(0,2) are two points on a circle with centre O (x,y). prove that x=y​

Answer 1

Answer:

${\bold{\therefore Coordinate\:of\:O=(1,1)}}$

Step-by-step explanation:

${\bold{\huge{\underline{SOLUTION-}}}}$

• In the given question information given about a circle whose two coordinate are on circle and one is the centre of circle.

• So, if we join the line O to point A or B It become radius of circle.

• Therefore, OA=OB.

• We have to find the Coordinate of O(x,y).

• To prove value of x = value of y

$\underline \bold{Given : } \\ \implies coordinate \: of \: A = (2,0) \\ \implies coordinate \: of \: B = (0,2) \\ \\ \underline \bold{To \: find : } \\ \implies coordinate \: of \: O= (x,y) \\ \\ \underline \bold{To \: Prove : } \\ \implies x = y$

• According to given question :

$\bold{By \: Mid \: point \: formula : } \\ \implies x = \frac{ x_{1} + x_{2} }{2} \\ \implies x = \frac{2+ 0}{2} \\ \bold{\implies x = 1} \\ \\ \implies y = \frac{ y_{1} + y_{2} }{2} \\ \implies y = \frac{0 + 2}{2} \\ \bold{\implies y = 1} \\ \\ \bold{Proof :} \\ \implies x = 1 - - - - - (1) \\ \implies y = 1 - - - - - (2) \\ \bold{From \: (1) \: and \: (2)} \\ \bold{\therefore x = y} \\ \: \: \: \: \bold {Proved}$

Answer 2

ANSWER:-

Given:

If A(2,0) & B(0,2) are two points on a circle with centre O(x,y).

To prove:

Prove that x=y.

Proof:

⚫Coordinate of A= (2,0)

⚫Coordinate of B= (0,2)

⚫Coordinate of O= (x,y)

We know that using the formula of midpoint ;

$= > x = \frac{x1 + y1}{2} \: \: and \: y = \frac{y1 + y2}{2}$

According to this question:

Coordinate of x;

$= > x = \frac{x1 + x2}{2} \\ \\ = > x = \frac{2 + 0}{2} \\ \\ = > 2x = 2 + 0 \\ \\ = > 2x = 2 \\ \\ = > x = \frac{2}{2} \\ \\ = > x = 1 ........(1)$

Coordinate of y:

$= > y = \frac{y1 + y2}{2} \\ \\ = > y = \frac{0 + 2}{2} \\ \\ = > 2y = 0 + 2 \\ \\ = > 2y = 2 \\ \\ = > y = \frac{2}{2} \\ \\ = > y = 1.......(2)$

Now,

From equation (1) & (2) we get;

=) x- y = 0

=) x = y

Hence,

Proved.

Hope it helps ☺️