Given the diagram below. If G is the circumcenter of ABC. DC = 16, GB = 21 and AZ = 19, find each measure.
1 answer:
Answer:
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
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Answer:
Center = (5,-3) and radius = 7
Step-by-step explanation:
(5) If Oskar bisects the diameter of a circle, what is he trying to construct the radius of the circle.
(6) The given equation is :
The general equation of circle is given by :
...(1)
Where
(a,b) are the coordinates of the centre and r is the radius.
The given equation can be written as :
..(2)
Comparing equation (1) and (2) we get :
a = 5, b = -3 and r = 7
So,
Center = (5,-3) and radius = 7
Hence, this is the required solution.