100 POINTS ⦁ Points D, E, and F are not in a line. To construct a circle through points D, E, and F, begin by drawing line segments and . Then construct the perpendicular bisectors of and , and name the point of intersection of the perpendicular bisectors O. How do you know that point O is the center of the circle that passes through the three points? (10 points)

O is the center of the circle with radius IE(=ID=EF)

Step-by-step explanation:

Join all 3 points D, E, F, forming the triangle DEF.

Let the midpoint of EF be M and the midpoint of ED be N. (first picture)

Join point I to E, D and F.

Since IN is both an altitude and median to triangle EID, then triangle EID is an isosceles triangle, and IE=ID

similarly, we see that IE=IF.

conclusion: IE=ID=EF.

set each factor equal to 0

4x-3 = 0

2x-1 = 0

solve for x.

4x-3=0

4x=3

x= 3/4

solve for x. 

2x-1= 0

2x= 1

x= 1/2

your answer should be 1/2 is less than or equal to x and 3/4 is greater than or equal to x

a

step-by-step explanation: