A triangle has corners at #(9 ,8 )#, #(2 ,3 )#, and #(7 ,4 )#. What is the area of the triangle's circumscribed circle?
1 Answer
Explanation:
The standard Cartesian form for the equation of a circle is:
Where
We can use the equation and the 3 points to write 3 equations:
Expand the squares:
Subtract equation [2.1] from equation [1.1]:
Write in standard form:
Subtract equation [2.1] from equation [3.1]:
Write as k in terms of h:
Substitute equation [5] into equation [4]:
Use equation [5] to find the value of k:
Use equation [1] to solve for
Because the area of a circle is:
We need only multiply by