An equilateral triangle with sides of length 6 is inscribed in a circle what is the diameter
1 answer:
Answer:
The diameter of the circumscribed circle is 6.92
Step-by-step explanation:
In the question, we are asked to calculate the diameter of a circle, which has a an equilateral triangle inscribed in it.
To solve this problem, let us consider the diagram attached.
Now let’s assume the point o is the center of the circle and that r is the radius of the circle. Now to calculate this radius, we need to employ the use of a trigonometrical ratio.
According to the question, we can see that we have the adjacent and the hypotenuse, so the trigonometric identity to use is the cosine.
Mathematically;
Cosine 30 = 3/r
r = 3/cosine 30
Cosine 30 = 0.866
r = 3/0.866
r = 3.46
But in the question, we were asked to calculate the diameter and not the radius.
Mathematically; d = 2r = 2 * 3.46 = 6.92
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Answer:
a). Center of the circle = (-2, 5)
b). Equation of the line ⇒ y =
Step-by-step explanation:
Equation of the circle is,
x² + 4x + y²- 10y + 20 = 30
a). [x² + 2(2)x + 4 - 4] + [y²- 2(5)y + 25] - 25 + 20 = 30
[x² + 2(2)x + 4] - 4 + [y² - 2(5)y + 25] - 25 + 20 = 30
(x + 2)² + (y - 5)²- 29 + 20 = 30
(x + 2)² + (y - 5)²- 9 = 30
(x + 2)² + (y - 5)² = 39
By comparing this equation with the standard equation of a circle,
Center of the circle is (-2, 5).
b). A point (2, 10) lies on this circle.
Slope of the line joining this point to the center (-2, 5),
=
=
Let the slope of the tangent which is perpendicular to this line is ''
Then by the property of perpendicular lines,
Now the equation of the line passing though (2, 10) having slope
y - y' =
y - 10 =
y - 10 =
y =
y =
Therefore, equation of the line will be, y =