Question

If the centre and radius of a circle is ( 3 , 4 ) and 7 units respectively, then what is the position of the point (5,8) with respect to the circle ? Please reply quickly. Thanks

Answer 1

Distance of the point, A from centre

= $\bf\huge\sqrt{(5 - 3)^2 + (8 - 4)^2$

= $\bf\huge\sqrt{4 + 16}$

= $\bf\huge\sqrt{20}$

= $\bf\huge 2\sqrt{5}$

2√5 is less than 7.  

∴ The point lies inside the circle

Answer 2

Point (5,8) lies inside the circle.

Given,

The center of the circle is (3,4) and the radius of the circle is 7 units.

To Find,

The position of the point (5,8) with respect to the circle.

Solution,

First, we will find the distance between the given point (5,8) and the center of the circle (3,4).

Distance = √(5-3)²+(8-4)²

Distance = √(2)²+(4)²

Distance = √20

Distance = 2√5 units

Now, 7(radius)>2√5

So, the point (5,8) will lie inside the circle because the radius of the circle is greater than the distance between the point and the center.

Hence, point (5,8) lies inside the circle.

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