A triangle has corners at #(5 ,6 )#, #(4 ,3 )#, and #(8 ,2 )#. What is the area of the triangle's circumscribed circle?
1 Answer
The area of the circumscribed circle is:
Explanation:
The standard Cartesian equation for a circle is:
where x and y correspond to any point,
Before I use equation [1] and the 3 given points to write 3 equation, I will shift all 3 points so that one of them is the origin,
Use equation [1] and the 3 shifted points to write 3 equations:
Equation [2] simplifies to:
We can temporarily eliminate the variable, r, by substituting the left side of equation [5] into the right sides of equations [3] and [4]:
Use the pattern,
Collect the constant terms into a single term on the right:
Multiply equation [13] by 3 and add to equation [12] and then solve for h:
Substitute
Substitute these values of h and k into equation [5] to obtain the value of
The area of a circle is:
The area of the circumscribed circle is: