Question

A triangle has vertices A (0,0), B(13,0)and C (5,7). The triangle is inscibed in a circle. What are the coordinates of the center of the circle? Express your answer in the form of (x,y) where "x" and "y" are common fraction.

Answer 1

pick 2 sides and find the midpoint of each
find the slope of the sides
create equation of the perpendicular bisectors
set equal and solve

Answer 2

AB is easy
MP is (6.5,0), m=0, eqn of perpendicular bisector is y=6.5

Answer 3

what about BC?

Answer 4

BC MP (13+5)/2,(0+7)/2 -->>> (9,3.5)

Answer 5

but how do i find the equation of the perpendicular bisector for this one?

Answer 6

m is -7/8
slope of the perpendicular is 8/7

Answer 7

(y-y(1))=m(x-x(1))

Answer 8

y(1)=3.5, x(1)=9, m= 8/7

Answer 9

You can get an equation for a line from either
A) 2 points
B) A point and the slope <-----that's what we have

Answer 10

is the slope of AC 7/5?

Answer 11

5/7 Rise/Run.......(difference in y's)/(difference in x's)
But you don't need AC
The intersection of two of these will be the same as the intersection of the three

Answer 12

ok