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The center of the circumscribed circle about a triangle is equidistant to the vertices of the inscribed triangle?
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What are the dimensions of an isosceles triangle of least area that can be circumscribed about a circle of radius r?
The isosceles triangle of least area that can be circumscribed about a circle of radius r turns out to be not just isosceles, but also equilateral. Each side has length 2r x ( 3 )0.5 . The area is r2 x (27)0.5 . Thanks are due to litotes for pointing out that the original answer did not actually answer the question ! tpm Since the equilateral triangle is also an isosceles triangle, we can say that at least area that can be circumscribed to a circle is the area of an equilateral triangle.If we are talking only for isosceles triangle where base has different length than two congruent sides, we can say that at least area circumscribed to a circle with radius r, is the area of an isosceles triangle whose base angles are very close to 60 degrees. Solution: Let say that the isosceles triangle ABC is circumscribed to a circle with radius r, where BA = BC. We know that the center of the circle inscribed to a triangle is the point of the intersection of the three angle bisectors of the triangle. Let draw these angle bisectors, and denote with D the point where the bisector drawn from the vertex, B, of the triangle, intersects the base AC. Since the triangle is an isosceles triangle, then BD bisects the base and it is perpendicular to the base. So that AD = DC, OD = r, and the triangles ADB and AOD are right triangles (O is the center of the circle). In the triangle ADB, we have:tan A = BD/AD, so that AD = BD/tan A In the triangle AOD, we have:tan A/2 = OD/AD, so that AD = r/tan A/2, and AC = 2r/tan A/2 Therefore,BD/tan A = r/tan A/2, andBD = (r tan A)/tan A/2 Area of triangle ABC = (1/2)(AC)(BD) = (1/2)(2r/ tan A/2)[(r tan A)/tan A/2] = (r2 tan A)/tan2 A/2 After we try different acute angles measure, we see that the smallest area would be: If the angle A= 60⁰,then the Area of the triangle ABC = r2 tan 60⁰/tan2 30⁰ ≈ 5.1961r2 If the angle A= 59.8⁰,then the Area of the triangle ABC = (r2 tan 59.8⁰)/tan2 29.9⁰ ≈ 5.1962r2
How do you calculate the area of a sphere?
The surface area of a sphere is 4 x pi x radius2 - exactly 4 times the area of the circle you get when you cut the the sphere right through the center.
What is the area of a triangle with base 12cm and height?
The formula to calculate the area of a triangle is 1/2 * base * height. To understand this, think of a rectangle or a square. To calculate the area of this object you would use length * width (which is the same as base * height). If you cut this object in half, you get a triangle. So that area of any triangle is 1/2 * base * height. I cannot answer your question because you are missing the triangle's height but you should be able to use the formula above to calculate the answer on your own.
What is sin y?
The Sine function (abbreviated sin) takes an angle and gives a ratio which is based on the sides of a right triangle. If you have a right triangle, and one of the angles (not the right angle) is labeled y then sin y equals the length of the side opposite of angle y divided by the length of the hypotenuse. The hypotenuse of a right triangle is the longest side, and is always opposite of the right angle.
What area of right triangle?
Area of a right angle triangle is: 0.5*base*height
What is the Area of a right angled triangle?
1/2*base of triangle*height(the perpendicular)=Area of right angled triangle
What is the area of right angled triangle at the right?
There is no right triangle on the right! (Ignore the length of the hypotenuse of a right triangle.) if you have the length of the two legs (base and the upright side): (base x upright) ÷ 2 = area of the right angle triangle.
How do l work out the area of a triangle?
A right triangle is easy, simply multiply the two sides and divide by two. A non-right triangle is a bit more of a challenge. You have to make it a right triangle by adding a right triangle to it. Calculate and then subtract the area of what you had to add.
How do you find the perimeter of a right angled triangle using the area?
how to find the perimeter of a right angled triangle using the area
What is the area of a 12cm by 5cm right-angled triangle?
The area of a 12cm by 5cm right-angled triangle is: 42 cm2
What is the formula to finding an area to a right triangle?
The area of any triangle is1/2 of (the length of the triangle's base) times (the triangle's height).
Area of a right triangle?
Area of a right triangle = (1/2 the length of one leg) x (length of the other leg)
Formula for area of a right triangle?
Area=1/2(base*height) where either side can be the base or the height in a right triangle.
If a right triangle has a hypotenuse of 10m and a base of 5mwhat is the area?
A right triangle with a hypotenuse of 10m and a base of 5m has an area of: 21.65m2
How do you find the area if you have a right angle triangle with all the mesurements?
The area of a right triangle is 1/2 of the product of the two legs.
What is the area of a right triangle that has legs 7 cm and 4 cm long?
The area of a right triangle that has legs 7 cm and 4 cm long can be calculated using the fact that a right triangle is half of a rectangle. The area of a rectangle is l*h, so the area of a right triangle is l*h/2. In this case, the area is 14 cm^2.
