Split the triangle into a 30-60-90 triangle. Since you have LM from that triangle, you can figure out the other sides. Then, using the leg from that triangle, the one next to it is a 45-45-90 triangle, meaning it's isosceles.
KM = 30 + 10√3
KL = 10√6
(sorry i'm not too sure if my "reasons" for statement/reason is correct)
Answer:
(x +6)^2 +(y +2)^2 = 72
Step-by-step explanation:
The given points are vertices of a right triangle. The circle circumscribing that triangle (through all 3 vertices) will have its center at the midpoint of the hypotenuse:
((0, 4) +(-12, -8))/2 = (-6, -2)
The equation of a circle with center (h, k) through point (a, b) is ...
(x -h)^2 +(y -k)^2 = (a -h)^2 +(b -k)^2
For center (-6, -2) and point (0, 4), the equation is ...
(x +6)^2 +(y +2)^2 = (0+6)^2 +(4 +2)^2
(x +6)^2 +(y +2)^2 = 72
