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jolli1 [7]
3 years ago
13

A circle is inscribed in a 40º-60º-80º triangle. The points of

Mathematics
1 answer:
Vladimir [108]3 years ago
3 0

Answer:

A = 50°

B = 60°

C = 70°

Step-by-step explanation:

If we draw a line from each vertex through the center of the circle, we perpendicularly bisect the line joining the adjacent tangent points.

We then know the original angle is halved and the remaining angle of each right triangle is complementary to half the original.

Now we can subtract the known angles along each line of the original side to find the remaining angle

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A circle is centered at the point (-3, 2) and passes through the point (1, 5). The radius of the circle is ___ units. The point
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Answer:

The radius is 5 units

(-7,-1) and (-7,5) lies on the circle

Step-by-step explanation:

Use the distance formula to find the distance between the center and the given point that gives you the radius.

d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}

The center is (-3,2) and the point on the circumference is (1,5)

r=\sqrt{(1--3)^2+(5-2)^2}

r=\sqrt{(4)^2+(3)^2}

r=\sqrt{16+9}

r=\sqrt{25}

\therefore r=5

The radius is 5 units.

The equation of the circle is given by:

(x--3)^2+(y-2)^2=5^2

(x+3)^2+(y-2)^2=25

When x=-7, we obtain y by substituting into the equation of the circle:

(-7+3)^2+(y-2)^2=25

(-4)^2+(y-2)^2=25

16+(y-2)^2=25

(y-2)^2=25-16

(y-2)^2=9

y-2=\pm \sqrt{9}

y=2\pm 3

y=-1 or y=5

Therefore (-7,-1) and (-7,5) lies on the circle.

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