70.1k views
4 votes
8. Find the center of the circle that can be circumscribed about the triangle.y-4-262-224

8. Find the center of the circle that can be circumscribed about the triangle.y-4-262-224-example-1
User PoeticGeek
by
6.3k points

1 Answer

7 votes

The labelled triangle is shown below

The required center is the point where the perpendicular bisectors meet. It is called the circumcenter. We would find it by applying the midpoint method. The midpoint formula is expressed as

midpoint, M(x, y) = (x1 + x2)/2, (y1 + y2)/2

For AB,

x1 = - 4, y1 = 0

x2 = 4, y2 = 0

Midpoint = (- 4 + 4)/2, (0 + 0)/2 = (0, 0)

For AC,

x1 = - 4, y1 = 0

x2 = 0, y2 = 4

Midpoint = (- 4 + 0)/2, (0 + 4)/2 = (- 2, 2)

For BC,

x1 = 4, y1 = 0

x2 = 0, y2 = 4

Midpoint = (4 + 0)/2, (0 + 4)/2 = (2, 2)

We woulf find the slope of AC

Slope, m = (y2 - y1)/(x2 - x1) = (4 - 0)/(0 - - 4) = 4/(0 + 4) = 4/4

m = 1

Slope of the line per

8. Find the center of the circle that can be circumscribed about the triangle.y-4-262-224-example-1
User Nick White
by
7.6k points