Given the diagram below. If G is the circumcenter of ABC. DC = 16, GB = 21 and AZ = 19, find each measure.

Step-by-step explanation:

Properties of a circumcenter;

1). Circumcenter of a triangle is a point which is equidistant from all vertices.

2). Point where perpendicular bisectors of the sides of a triangle meet is called circumcenter of the triangle.

From the picture attached,

9). AG = GB = GC = 21

10). BC = 2(DC)

            = 2×16

            = 32

11). By applying Pythagoras Theorem in ΔGFB,

     GB² = GF² + FB²

     (21)² = GF² + (19)²

     441 = GF² + 361

     GF² = 441 - 361

     GF =

     GF = 8.9

12). By applying Pythagoras theorem in ΔGDB,

     GB² = DG² + BD²

     (21)² = (DG)² + (16)² [BD = DC = 16]

     DG² = 441 - 256

     DG = √185

     DG =  13.6

x > 1.3

step by step:

8.5−0.9x> 9.8−1.9x

step 1: simplify both sides of the inequality.

−0.9x+8.5> −1.9x+9.8

step 2: add 1.9x to both sides.

−0.9x+8.5+1.9x> −1.9x+9.8+1.9x

1x+8.5> 9.8

step 3: subtract 8.5 from both sides.

1x+8.5−8.5> 9.8−8.5

1x> 1.3

step 4: divide both sides by 1.

1x/1 > 1.3/1

if you was gonna solve for a, a is a   < -12