Question

if the centre and radius of a circle is (3,4) and 7 units respectively then what is the position of. A (5,8) with respect to the circle

Answer 1

Given:
C(3,4)
Radius = 7 units
A(5,8)

We will find distance AC. If it is less than the radius, the point is in the circle. If it is greater than the radius the point is outside the circle and if it is equal to the radius the point is on the circle.

AC = {(8-4)² + (5-3)²}^0.5
AC = {16 + 4}^0.5
AC = √20 ≈ 4.47 units

Since AC < 7, i.e. the radius of the circle, thus point A lies inside the circle.

Answer 2

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