Question

Circle O is centered at the origin. Point P (1,^3) lies on the circle. What is the radius of the circle?A. 1 unitB. 2 unitsC. 3 unitsD. 4 units

Answer 1

The circle with its origin at 0, and a point (1, V3) means all points along the circle is the same distance from point zero (origin). From the information provided we can deduce a right angled triangle as shown below.

The points given as

`P(1,\sqrt[]{3})`

means that point P is 1 unit along the x-axis and square root 3 units along the y-axis. Note that the distance between point P and the origin is the radius. We can now solve for the radius by using the Pythagoras' theorem;

`\begin{gathered} a^2=b^2+c^2 \\ \text{Where, a=hypotenuse, b and c=other two sides} \\ r^2=1^2+(\sqrt[]{3})^2 \\ r^2=1+(\sqrt[]{3}*\sqrt[]{3}) \\ r^2=1+3 \\ r^2=4 \\ r=\sqrt[]{4} \\ r=2 \end{gathered}`

The radius of the circle is 2 units

Option B is the correct answer