Question

find the diameter of circle whose centre is origin of axis & one point on circle is (1,1)​

Answer 1

$\tt\blue{\underline{Answer:}}$

$\green{\tt\therefore Diameter \: of \: circle = 2 \sqrt{2} \: units}$

$\tt \green{\underline{Given : }} \\ \tt: \implies Centre \: of \: circle = (0,0) \\ \\ \tt: \implies Point \: on \: circle = (1,1) \\ \\ \tt \red{\underline{ To \: Find : }} \\ \tt: \implies Diameter \: of \: circle =?$

$\tt\orange{\underline{Step-by-step\:\:explanation:}}$

• According to given question :

$\circ \: \sf Let \: centre \: be \: C = (0,0) \\ \\ \sf\circ \: point \: on \: the \: circle \: A= (1,1)\\ \\ \bold{As \: we \: know \: that} \\ \tt: \implies AC = \sqrt{(x_{2} - x_{1})^{2} + ( y_{2} - y_{1} )^{2} } \\ \\ \tt: \implies AC= \sqrt{(1 - 0)^{2} + {(1 - 0)}^{2} } \\ \\ \tt: \implies AC= \sqrt{1 + 1} \\ \\ \tt: \implies AC = \sqrt{2} \: units \\ \\ \sf\because \: AC = Radius \: of \: circle \\ \\ \sf \green{\therefore Diameter \: of \: circle = 2R= 2 \sqrt{2} \: units}$

Answer 2

$\small\bold\red{Given:-}$

• Centre of circle = ( 0 , 0 )
• Point on circle = ( 1 , 1 )

$\small\bold\green{To \: Find:-}$

• Diameter of circle .

$\small\bold\pink{Solution:-}$

• Let the Centre C = ( 0 , 0 )
• Point on the circle A =( 1 , 1 )

$\small\bold{Radius \: of \: the \: circle \: AC =}$

$= \sqrt{ {(1 - 0})^{2} + {(1 - 0)}^{2} } \\ = \sqrt{1 + 1 } \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ = \sqrt{2 \:} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

Hence ,

• AC = 2

$\small\bold{diameter \: of \: circle = 2r = 2 \sqrt{2} units}$