A day full of math games & activities. Find one near you.

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. Is the following statement true or false

Solution:

Given, the centre of the circle is at the origin.

Point P(5, 0) lies on the circle.

We have to determine if the point Q(6, 8) lies outside the circle.

We know that, if the distance of any point from the centre is

less than the radius, then the point is inside the circle
equal to the radius, then the point is on the circle.
more than the radius, then the point is outside the circle.

To find the radius of the circle,

Radius of the circle is equal to the distance between the origin and the point P(5, 0)

The distance between two points P (x₁ , y₁) and Q (x₂ , y₂) is

√[(x₂ - x₁)²+(y₂ - y₁)²]

So, OP = radius of the circle = √[(5 - 0)²+(0 - 0)²]

= √[(5)²+0]

= √25

OP = 5

Distance between the origin and Q(6, 8) = √[(6 - 0)²+(8 - 0)²]

= √[(6)²+(8)²]

= √(36 + 64)

= √100

OQ = 10

We observe that OQ > OP

The distance of the point OQ is greater than the radius of the circle.

Therefore, the point Q lies outside the circle.

✦ Try This: Determine if the circle with its centre at the origin and a point P (8, 0) lies on it. The point Q (6, 9) lies outside the circle.

☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 7

NCERT Exemplar Class 10 Maths Exercise 7.2 Problem 7

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. Is the following statement true or false

Summary:

The statement “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” is true as the distance OQ is greater than the radius of the circle

☛ Related Questions: