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Two vertices of the triangle and the centre of the circle make a smaller equilateral triangle with legs of 4 cm and the included angle is 360/3 = 120 degrees.
Therefore the area of each of these sub-triangles = 1/2*ab*sin(C) = 1/2*4*4*sin(120) = 1/2*4*4*1/2 = 4 cm2.
And so the area of the inscribed triangle is 12 cm2.
Two vertices of the triangle and the centre of the circle make a smaller equilateral triangle with legs of 4 cm and the included angle is 360/3 = 120 degrees.
Therefore the area of each of these sub-triangles = 1/2*ab*sin(C) = 1/2*4*4*sin(120) = 1/2*4*4*1/2 = 4 cm2.
And so the area of the inscribed triangle is 12 cm2.
Two vertices of the triangle and the centre of the circle make a smaller equilateral triangle with legs of 4 cm and the included angle is 360/3 = 120 degrees.
Therefore the area of each of these sub-triangles = 1/2*ab*sin(C) = 1/2*4*4*sin(120) = 1/2*4*4*1/2 = 4 cm2.
And so the area of the inscribed triangle is 12 cm2.
Two vertices of the triangle and the centre of the circle make a smaller equilateral triangle with legs of 4 cm and the included angle is 360/3 = 120 degrees.
Therefore the area of each of these sub-triangles = 1/2*ab*sin(C) = 1/2*4*4*sin(120) = 1/2*4*4*1/2 = 4 cm2.
And so the area of the inscribed triangle is 12 cm2.
What else can I help you with?
The radius of a incircle is 14cm what is the side of the equilateral triangle abc?
Where the side of the equilateral triangle is s and the radius of the inscribed circle is r:s = 2r * tan 30° = 48.50 cm
Mateo is constructing an equilateral triangle inscribed in a circle with center P. What is his first step?
Mateo's first step in constructing an equilateral triangle inscribed in a circle with center P is to draw the circle itself, ensuring that the radius is defined. Next, he can mark a point on the circumference of the circle to serve as one vertex of the triangle. From there, he will need to use a compass to find the other two vertices by measuring the same distance (the length of the triangle's side) along the circumference of the circle. Finally, he will connect the three points to form the equilateral triangle.
The shortest distance from the center of the inscribed circle to the triangle's sides is the circle's?
radius
Is it true or false that the radius of the circle inscribed an equilateral triangle equals one-half the length of the length of the triangles median?
This is true. The answer is obvious if you think about it the following way: an equilateral triangle has three equal sides, and every point on the circumference of a circle is the same distance from the center of the circle. Therefore, it is safe to assume that the circle will touch the midpoint of each side of the triangle. It also means that the center of the circle will be in the center of the triangle. Therefore, the radius of the circle will travel from the center of the triangle to the midpoint of one of the sides. This will cover the distance of half the triangle's median.
Does a triangle have a radius?
It has at least two radii, the radius of the circle going through the vertices and the radius of the inscribed circle touching all the sides.
The radius of a incircle is 14cm what is the side of the equilateral triangle abc?
Where the side of the equilateral triangle is s and the radius of the inscribed circle is r:s = 2r * tan 30° = 48.50 cm
Mateo is constructing an equilateral triangle inscribed in a circle with center P. What is his first step?
Mateo's first step in constructing an equilateral triangle inscribed in a circle with center P is to draw the circle itself, ensuring that the radius is defined. Next, he can mark a point on the circumference of the circle to serve as one vertex of the triangle. From there, he will need to use a compass to find the other two vertices by measuring the same distance (the length of the triangle's side) along the circumference of the circle. Finally, he will connect the three points to form the equilateral triangle.
The shortest distance from the center of the inscribed circle to the triangle's sides is the circle's?
radius
Is it true or false that the radius of the circle inscribed an equilateral triangle equals one-half the length of the length of the triangles median?
This is true. The answer is obvious if you think about it the following way: an equilateral triangle has three equal sides, and every point on the circumference of a circle is the same distance from the center of the circle. Therefore, it is safe to assume that the circle will touch the midpoint of each side of the triangle. It also means that the center of the circle will be in the center of the triangle. Therefore, the radius of the circle will travel from the center of the triangle to the midpoint of one of the sides. This will cover the distance of half the triangle's median.
Does a triangle have a radius?
It has at least two radii, the radius of the circle going through the vertices and the radius of the inscribed circle touching all the sides.
The shortest distance from the center of the circumscribed circle to the vertices of the inscribed triangle is the circle's radius?
True
What is the formula for equillateral triangle?
There are different formula for: Height, Area, Perimeter, Angle, Length of Median Radius of inscribed circle Perimeter of inscribed circle Area of inscribed circle etc.
How do you inscribe a circle in a triangle?
To inscribe a circle in a triangle, first, find the triangle's three angle bisectors. The point where these bisectors intersect is called the incenter, which serves as the center of the inscribed circle. Next, measure the perpendicular distance from the incenter to any side of the triangle; this distance is the radius of the inscribed circle. Finally, draw the circle using the incenter as the center and the measured radius.
An equilateral triangle surrounds a circle of radius 10 cm and is itself surrounded by a larger circle Find the radius of the bigger circle?
Make a sketch of the situation. From a corner of the equilateral triangle draw a radius of the large circle, and from an adjacent side draw a radius of the smaller circle. You should have formed a small right-angled triangle with a known side of 10cm. and known angles of 30o, 60o and 90o. (The interior angles of an equilateral triangle are each 60o.) The hypotenuse is the unknown radius of the larger circle. But since cos 60 = 0.5, it is evident that the hypotenuse is 20cm. long.
The shortest distance from the center of the circumscribed circle to the sides of the inscribed triangle is the circles radius?
FALSE
Is the shortest distance from the center of the circumscribed circle to the vertices of the inscribed triangle is the circles radius?
True
Which step do the constructions of a regular hexagon a square and an equilateral triangle inscribed in a circle all have in common?
The common step in the constructions of a regular hexagon, a square, and an equilateral triangle inscribed in a circle is the process of drawing the circle itself, which serves as the circumcircle for all three shapes. After establishing the circle's center and radius, each shape can be constructed by dividing the circle's circumference into equal segments or angles, allowing for the accurate placement of vertices. This foundational step ensures that all vertices of the shapes are equidistant from the center, maintaining their regularity.
