Question

The radius of a circle with centre at origin is 30 units. If the circle intersects the coordinate axes at ‘a’ and ‘b’ respectively, find the distance between the two points.

• A. $16\text{units}$
• B. $22\text{units}$
• C. $25\sqrt{3}\text{units}$
• D. $30\sqrt{2}\text{units}$

Answer 1

The correct option is D $30\sqrt{2}\text{units}$

Radius of the circle = 30 units.
The point O is (0, 0).

Since, a intersect the x-axis and b intersect the y-axis.
∴ The point A is (a, 0) and B is (0, b)

Distance $=\sqrt{\left[\right(x_2-x_1{)}^2+(y_2-y_1{)}^2]}$
$\Rightarrow OA=\sqrt{\left[\right(a-0{)}^2+(0-0{)}^2]}$
$\Rightarrow 30=\sqrt{a^2}$
$\Rightarrow a=30$ units

The point A is (30, 0)

Now, $OA=\sqrt{\left[\right(0-0{)}^2+(b-0{)}^2]}$
$\Rightarrow 30=\sqrt{b^2}$
$\Rightarrow b=30$ units

The point B is (0, 30)

Hence, distance between point A and Point B is
$AB=\sqrt{\left[\right(30-0{)}^2+(0-30{)}^2]}$
$AB=\sqrt{({30}^2+{30}^2)}$
$AB=30\sqrt{2}$ units