Question

A circle has its centre at the origin and a point P(5, 0) lies on it. The point Q(6, 8) lies outside the circle.

Options

• True

• False

Answer 1

This statement is True.

Explanation:

First, we draw a circle and a point from the given information

Now, distance between origin i.e., O(0, 0) and P(5, 0),

OP = `sqrt((x_2 - x_1)^2 + (y_2 - y_1)^2`

OP = `sqrt((5 - 0)^2 + (0 - 0)^2` 

= `sqrt(5^2 + 0^2)`

= 5

= Radius of circle and distance between origin O(0, 0) and Q(6, 8),

OQ = `sqrt((6 - 0)^2 + (8 - 0)^2`

= `sqrt(6^2 + 8^2)`

= `sqrt(36 + 64)`

= `sqrt(100)`

= 10

We know that, if the distance of any point from the centre is less than/equal to/more than the radius, then the point is inside/on/outside the circle, respectively.

Here, we see that, OQ > OP

Hence, it is true that point Q(6, 8), lies outside the circle.