Question

In the given figure, a circle is centred at (1, 2). The diameter of the circle is

Options

• 4

• `2sqrt(2)`

• `sqrt(5)`

• `2sqrt(5)`

Answer 1

`bb(2sqrt(5))`

Explanation:

Radius r = distance between center (1, 2) and origin (0, 0).

Diameter D = 2r.

Distance formula: `d = sqrt((x_2 - x_1)^2 + (y_2 - y_1)^2`

`r = sqrt((1 - 0)^2 + (2 - 0)^2`

`r = sqrt(1^2 + 2^2)`

= `sqrt(1 + 4)`

= `sqrt(5)`

Diameter (D) = `2 xx sqrt(5)`

= `2sqrt(5)`

 The diameter of the circle is `2sqrt(5)`.