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What is the radius of an equilateral triangle?

The radius of a circumcircle of an equilateral triangle is equal to (a / √3), where ‘a’ is the length of the side of equilateral triangle.

Do equilateral triangles have equal sides?

An equilateral triangle has three equal sides, as can be deduced from its name. This also means that as a result, the triangle is also equiangular. That is, all its interior angles are the same. Because the sum of internal angles of a triangle is , that means that each interior angle is .

Can an equilateral triangle be inscribed in a circle?

We can continue drawing circles, with centers P and Q and each time we get another equilateral triangle. The end result will be a regular hexagon inscribed inside the circle: joining every other vertex of this hexagon gives an equilateral triangle inscribed in the circle.

What is the side of an equilateral triangle inscribed in a circle?

i) Since the triangle is Equilateral (side S = 6 cm), it’s Perpendicular Bisector (Altitude) = Median = Angle Bisectors. And all meet at the same point (O). ii) In order to inscribe a triangle within a circle, the Centre of the Circle should be the Circum-centre (that is where the perpendicular bisectors meet).

How do you solve a triangle inscribed in a circle?

Given A, B, and C as the sides of the triangle and A as the area, the formula for the radius of a circle circumscribing a triangle is r = ABC / 4A and for a circle inscribed in a triangle is r = A / S where S = (A + B + C) / 2.

What is the radius of a circle inscribed in a triangle?

For any triangle △ABC, let s = 12 (a+b+c). Then the radius r of its inscribed circle is r=Ks=√s(s−a)(s−b)(s−c)s. Recall from geometry how to bisect an angle: use a compass centered at the vertex to draw an arc that intersects the sides of the angle at two points.

What is the formula for radius of curvature?

The radius of curvature of a curve at a point M(x,y) is called the inverse of the curvature K of the curve at this point: R=1K. Hence for plane curves given by the explicit equation y=f(x), the radius of curvature at a point M(x,y) is given by the following expression: R=[1+(y′(x))2]32|y′′(x)|.

What is the radius of curvature of the mirror?

A spherical lens or mirror surface has a center of curvature located either along or decentered from the system local optical axis. The vertex of the lens surface is located on the local optical axis. The distance from the vertex to the center of curvature is the radius of curvature of the surface.

What is the radius of curvature of a straight line?

infinity

How do you find the radius of curvature of a mirror?

R=CF+FP. In other words, in the small-angle approximation, the focal length f of a concave spherical mirror is half of its radius of curvature, R: f=R2.

What is the mirror formula?

Suppose an object is placed u cm in front of a spherical mirror of focal length f such that the image is formed v cm from the mirror, then u, v and f are related by the equation; 1/f= 1/u + 1/v. This equation is referred to as the mirror formula. The formula holds for both concave and convex mirrors.

What is the relation between the radius of curvature and the focal length of a mirror?

The focal length of a spherical mirror is then approximately half its radius of curvature. It is important to note up front that this is an approximately true relationship.

What is the definition of radius of curvature?

In differential geometry, the radius of curvature, R, is the reciprocal of the curvature. For a curve, it equals the radius of the circular arc which best approximates the curve at that point. For surfaces, the radius of curvature is the radius of a circle that best fits a normal section or combinations thereof.

What is minimum radius of curvature?

The minimum curve radius is a limiting value of curvature for a given design speed. In the design of horizontal alignment, smaller than the calculated boundary value of minimum curve radius cannot be used. Thus, the minimum radius of curvature is a significant value in alignment design.

What is the name of the radius?

The distance from the pole is called the radial coordinate or radius, and the angle is the angular coordinate, polar angle, or azimuth.

Where is the radius located on a circle?

The Radius is the distance from the center outwards. The Diameter goes straight across the circle, through the center. The Circumference is the distance once around the circle.

since all sides of an equilateral triangle are equal.

It’s key to know that an equilateral triangle has equal sides and equal angles measuring 60 degrees each. So each angle of an equilateral triangle inscribed in a circle cuts off 1/3 of the circle.

How do you find the length of the side of an equilateral triangle?

Explanation: Since each of this triangle’s sides is equal in length, it is equilateral. To find the length of one side of an equilateral triangle, we need to divide the perimeter by .

What is the length of the sides in an equilateral triangle?

An equilateral triangle is a special case of a triangle where all 3 sides have equal length and all 3 angles are equal to 60 degrees.

What is the length of the radius of the circle?

Answer: The radius is half the length of the diameter. We will use the definition of the radius of circle. Explanation: The definition of radius of a circle is the length of the line segment from the center of a circle to a point on the circumference of the circle. So, the radius is half the length of the diameter.

What is double the radius called?

By extension, the diameter d is defined as twice the radius: If an object does not have a center, the term may refer to its circumradius, the radius of its circumscribed circle or circumscribed sphere.

How does radius affect area?

In two dimensions the answer is simply: as the radius increases, the area increases by the square of the increasing factor. That’s a bit abstract, so let’s give some examples. If the radius doubles, that’s a factor of 2. The square of 2 is 4, so if the radius doubles the area is multiplied by 4.

What happens when you triple the radius?

If the radius is r, then the circumference is 2πr. If the radius r is tripled it becomes 3r. The circumference will then be 2π(3r) = 3(2πr). If the radius of a Circle is tripled, then its diameter is also tripled, and subsequently, its circumference is also tripled.

How do you find the radius when given the area?

The area of a circle is pi times the radius squared (A = π r²).

Do you square the radius first?

The correct interpretation is to first square the radius and then multiply by pi. Thus for your circle with diameter 4 inches the area is 3.1416 (2×2) = 12.5664 square inches.