Question

Points X=(0,0), Y=(6,10) and Z=(12,0 ) are given. How many units are in the length of the radius of the circle which passes through the points X,Y and Z? Express your answer to the nearest tenth.

Answer 1

What have you attempted?

Answer 2

lol nothing again, still the same kind of question.

Answer 3

I see, why not ask your teach for the answers then? Surely he or she would not mind as you are asking for knowledge. :-)

Answer 4

My teacher did give us the answer just not how we get to the answers :(

Answer 5

Well what is the answer then, so I can make sure you are not cheating an just explain it.

Answer 6

6.8 :3

Answer 7

All right, I see. Give me a moment to write the explanation.

Answer 8

The centre of the circle is the intersections of the perpendicular bisectors of XY and XZ.

The equation of the perpendicular bisector of XY is:
$$y = -(\dfrac{3}{5}) x + \dfrac{34}{5}$$

The equation of the perpendicular bisector of XZ is:
$$x = 6$$
The coordinates of the circle are \(C = (6, \dfrac{16}{5}\)).

\(\textbf{Hence:}\)
$$OC = \sqrt{(6^2 + (\dfrac{16}{5})^2)}= 6.8$$
Note: Answer was rounded to the nearest tenth.

Answer 9

Thanks!

Answer 10

You are welcome.