Question

If point A(4,3) and B(x,5),lines of a circel with 0(2,3),find x?

Answer 1

Point A & B lies on the circle with centre O
so AO=BO (both are radii of circle)

Using distance formula
√[(4-2)²+(3-3)²] = √[(x-2)²+(5-3)²]
Squaring both sides
(4-2)²+(3-3)² = (x-2)²+(5-3)²
4+0 = (x-2)²+4
(x-2)²=0
Answer:- x =2

Answer 2

OA=OB
(4-2)power 2 +(3-3)power 2=(x-2)power 2 +(5-3)power 2
(2)power 2=(x-2)power 2 +(2)power 2
4=4+(x-2)power 2
0=x*x+4-4x
x*x-4x+4=0
x*x-2x-2x+4=0
x(x-2)-2(x-2)=0
(x-2)(x-2)=0
x=2 or x=2