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Goryan [66]
2 years ago
11

Find the value of AB. 10 6 A E B AB = [?]

Mathematics
1 answer:
Nana76 [90]2 years ago
5 0

Answer:

AB = 16

Step-by-step explanation:

The radius of the circle = 10

From the center of the circle to B = 10 (radius)

Since a right angle is formed at point E, we can apply Pythagorean theorem to find EB.

Thus:

EB² = 10² - 6²

EB² = 100 - 36

EB² = 64

EB = √64

EB = 8

EB = AE = 8

therefore,

AB = AE + EB = 8 + 8

AB = 16

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Triangles abc, dbe, and fbg are all symmetric about the y-axis. what are the coordinates of the centroid?
Drupady [299]

Answer:

The coordinates of the centroid are (0, 5)

Step-by-step explanation:

The coordinates of the centroid of a triangle whose vertices (x1, y1), (x2, y2), and (x3, y3) are (\frac{x1+x2+x3}{3} , \frac{y1+y2+y3}{3})

In Δ ABC

∵ A = (-20, 0), B = (0, 15), C = (20, 0)

∴ x1 = -20, x2 = 0, x3 = 20

∴ y1 = 0, y2 = 15, y3 = 0

∴ The centroid = (\frac{-20+0+20}{3} , \frac{0+15+0}{3}) = (\frac{0}{3} , \frac{15}{3}) = (0, 5)

∴ The coordinates of the centroid of Δ ABC are (0, 5)

In Δ DBE

∵ D = (-15, 0), B = (0, 15), E = (15, 0)

∴ x1 = -15, x2 = 0, x3 = 15

∴ y1 = 0, y2 = 15, y3 = 0

∴ The centroid = (\frac{-15+0+15}{3} , \frac{0+15+0}{3}) = (\frac{0}{3} , \frac{15}{3}) = (0, 5)

∴ The coordinates of the centroid of Δ DBE are (0, 5)

In Δ FBG

∵ F = (-5, 0), B = (0, 15), G = (5, 0)

∴ x1 = -5, x2 = 0, x3 = 5

∴ y1 = 0, y2 = 15, y3 = 0

∴ The centroid = (\frac{-5+0+5}{3} , \frac{0+15+0}{3}) = (\frac{0}{3} , \frac{15}{3}) = (0, 5)

∴ The coordinates of the centroid of Δ FBG are (0, 5)

∵ The three triangles are symmetric about the y-axis

→ That means they have the same centroid and it lies on the y-axis

∴ The coordinates of the centroid are (0, 5)

8 0
2 years ago
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