Question

$(1,4)$ and $(3,8)$ are the end points of diameter of a circle. Find the radius and center of this circle.

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

Answer 1

The correct option is B

√5 and (2,6)

We can see that 0, the center of the circle, is the mid-point of A and B. Also, AB is twice the radius.

$\Rightarrow 0\equiv (\frac{1+3}{2},\frac{4+8}{2})$

=$(2,6)$

Radius $=\frac{1}{2}AB=\frac{1}{2}\sqrt{(3-1{)}^2+(8-4{)}^2}$

$=\frac{1}{2}\sqrt{4+16}$

$=\sqrt{5}$