A triangle has corners at #(9 ,7 )#, #(2 ,1 )#, and #(5 ,4 )#. What is the area of the triangle's circumscribed circle?
2 Answers
The area of the circle is aproximately
Explanation:
First things first, let us visualise the points we have:
These points may look collinear, but they are not.
Now, let's draw the triangle:
And finally, the circle:
We can finally start applying formulae and such.
The area of a circle, denoted
In our case, the radius we search is the radius of the circumscribed triangle,
But how do we find
So we must find one of the sides and the sine of its opposite angle, say
The line
So we have found
and its analogues. We are doing this to find the value of
We got to find
We can see that
From the Fundamental property of Trigonometry, we have:
If you're wondering why
Finally, we can find
So the area of the circle,
Points
Explanation:
There's just never any need to write a square root. Let's check the other answer.
I don't know why these questions refer to a triangle or its "corners," that is, its vertices. How about:
What's the area of the circle through
In this answer of mine we find
where
The denominator is actually sixteen times the squared area of the triangle. We get the squared lengths from the coordinates with no fuss:
That looks a bit different from the other, featured answer. (EDIT: It had
Just eyeballing the figure in the other answer,