Question

A circle having its centre at (0,0) has a point (3,4) on its boundary. Which of the following points will lie inside the circle?

• A. (5, 4)
• B. (6, 4)
• C. (2, 5)
• D. (2, 4)

Answer 1

The correct option is D (2, 4)


In the given figure, if a point lies on the circle, then using the Pythagoras theorem:

$x^2+y^2=r^2$

If a point (x, y) lies inside the circle, then:

$x^2+y^2<r^2$

If a point (x, y) lies ouside the circle, then:

$x^2+y^2>r^2$

For point (3, 4) whiles lies one the circle, we see:

$3^2+4^2=r^2$

$\Rightarrow 9+16=r^2$

$\Rightarrow r^2=25$

$\Rightarrow r=\sqrt{25}=5$

If the distance is less than 5 from the center, then it will lie inside the circle.

From the given points in the options, only option 'c' has the point (2, 4) for which the distance is $\sqrt{20}$ which is less than 5.

So, only option 'c' is correct.