Question

The center of the circle is at the origin and its radius is $10$. Which of the following points lies inside the circle?

• A. $(6,8)$
• B. $(0,11)$
• C. $(-10,0)$
• D. $(7,7)$

Answer 1

The correct option is D $(7,7)$

Distance between two points $(x_1,y_1)$ and $(x_2,y_2)$ can be calculated using the formula

$\sqrt{{(x_2-x_1)}^2+{(y_2-y_1)}^2}$.

Distance between the points Centre $(0,0)$ and $(6,8)=\sqrt{(6-0{)}^2+(8-0{)}^2}=\sqrt{100}=10$

Distance between the points Centre $(0,0)$ and $(0,11)=\sqrt{{(0-0)}^2+{(11-0)}^2}=\sqrt{121}=11$

Distance between the points Centre $(0,0)$ and $(-10,0)=\sqrt{{(-10-0)}^2+{(0-0)}^2}=\sqrt{100}=10$
Distance between the points Centre $(0,0)$ and $(7,7)=\sqrt{{(7-0)}^2+{(7-0)}^2}=\sqrt{49+49}=7\sqrt{2}$
Only the distance between the centre and $(7,7)$ is less than the radius $10$. Hence, $(7,7)$ lies inside the circle.