Question

if the point A 4, 3 and b x, 5 lie on the circle with Centre o 2, 3 find the value of x​

Answer 1

Answer:

Step-by-step explanation:

point A(4,3)

point B (X,5)

CENTER O (2,3)

DISTANCE BETWEEN A AND O

\sqrt{(4 - 2) {}^{2} + (3 - 3) {}^{2} } \\ \sqrt{(2 {)}^{2} } \\ distance \: between \: a \: and \: b \: is \: \\ 2 \: units

distance between B and O is

\sqrt{(x - 2) {}^{2} + (5 - 3) {}^{2} } = 2 \\ (x - 2) {}^{2} + (2) {}^{2} = (2) {}^{2} \\ {x}^{2} - 4x + 4 + 4 = 4 \\ {x}^{2} - 4x + 4 = 0 \\ (by \: factorization) \\ {x}^{2} - 2x - 2x + 4 = 0 \\ ............ \\ .....(x - 2)(x - 2) = 0 \\ value \: of \: x \: is \: 2

Answer 2

Answer:

A(4,3) B(X,5) O(2,3)

OA=OB

OA²=OB²

OA²=(4-2)²+(3-3)²

=4

OB²=(2-x)²+(3-5)²

=4+x²-4x+4

=x²-4x+8

OA²=OB²

4=x²-4x+8

x²-4x+4=0

(x-2)²=0

x=2