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Dimensions of an isosceles triangle of largest area that can be inscribed in a circle of radius r?
Wiki User
∙ 16y ago
The largest possible triangle is an equilateral triangle. Here's a sort of proof - try making some sketches to get the idea. * For any given isosceles triangle ABC that you might inscribe, where AB = BC... * ...Moving vertex A to be perpendicularly above the midpoint of BC will increase the area, since its distance from BC (the height of the triangle) will be at a maximum.* This gives a new isosceles, where AB = AC. * The same thing applies to the new isosceles. You can keep increasing the area in this way until the process makes no difference. If the process can increase the area no further, it can only be because all the vertices are already above the midpoints of the opposite edges. Which means we have an equilateral triangle. Anyhow, to answer the question, an equilateral triangle inscribed in a circle of radius r will have side length d where d2 = 2r2 - 2r2cos(120) from the cosine rule. and since cos(120) = -1/2 d2 = 2r2 + r2 = 3r2 and so d = r sqrt(3) *Equally, move vertex C above the midpoint of AB.
Wiki User
∙ 16y ago
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Find the dimensions of the rectangle of largest area that can be inscribed in a circle of radius a in C programming?
Find the dimensions of the rectangle of largest area that can be inscribed in a circle of radius a in C programming
What is the measure of the largest exterior angle of an isosceles right angle?
A isosceles right angle triangle will have 2 equal interior angles of 45 degrees and 1 angle of 90 degrees with its largest exterior angle being 180 -45 = 135 degrees.
If the largest angle of an isosceles triangle measures 106 find the measure of the smallest angle?
The smallest angle would be = 38 degrees. Proof: Base angles of an isosceles triangle must equ All angles of the triangle must add up to 180 degress considering that the known angle is not under 89 degrees the other two must equal, yet both add up to 76 degrees.
How can you determine which angle is the largest in a triangle?
The largest angle in a triangle is opposite to its longest side
In a scalene triangle the longest side is opposite the angle with the largest measure true of false?
True. In any triangle, the longest side is always opposite the largest angle; the shortest side is always opposite the shortest angle; and the middle length side is always opposite the middle size angle. In an isosceles triangle, there is no middle length side; and the two sides of equal length are opposite the angles of equal size. In an equilateral triangle, all sides are the same length, as are all the angles.
Find the dimensions of the rectangle of largest area that can be inscribed in a circle of radius a in C programming?
Find the dimensions of the rectangle of largest area that can be inscribed in a circle of radius a in C programming
What is the measure of the largest exterior angle of an isosceles right triangle?
135 degrees.
Find the dimensions of the rectangle of largest area that can be inscribed in a circle of radius 4 inches?
Approximately 5.66x5.66 in. Or root32 x root32
What is the measure of the largest exterior angle of an isosceles right angle?
A isosceles right angle triangle will have 2 equal interior angles of 45 degrees and 1 angle of 90 degrees with its largest exterior angle being 180 -45 = 135 degrees.
How is a right triangle and scalene triangle different?
A scalene specifies that no two sides and no two angles are equal. A right triangle has one side that is a right or 90 degree angle. A scalene triangle can be a right triangle {a 3-4-5 right triangle or a 30°-60°-90° right triangle, for example}. A scalene triangle can also be an acute or obtuse triangle. Note this: there is only one case of a right triangle, which is non-scalene. This is the isosceles right triangle with angles 45°, 45° & 90°, and sides sqrt(2), 1 & 1. All other right triangles are scalene. The terms scalene, isosceles, and equilateral refer to how the side lengths are related to each other. The terms right, acute and obtuse refer to angles, specifically the largest angle: obtuse - the largest angle is greater than 90°; right - the largest angle equals 90°; acute - the largest angle is less than 90°. The terms referring to angles are not necessarily mutually exclusive with the terms, which refer to side lengths (except for equilateral). So you can have an isosceles obtuse (a shallow pitched roof), or isosceles right (example above), or isosceles acute (a very steep pitched roof).
Which lines do you draw to find the center of a circle inscribed in a triangle?
In geometry, the incircle or inscribed circle of a triangle is the largest circle contained in the triangle; it touches (is tangent to) the three sides.The center of the incircle is called the triangle's incenter.The center of the incircle can be found as the intersection of the three internal angle bisectors.You draw three lines. Each line from one triangle head point to the opposite triangle side and bisecting the angle. These three lines will intersect in one point which is the circle center.
In an isosceles triangle are the base angles the biggest?
The two base angles are equal to one another. They may either be the two smallest, or the two largest, angles.
What are some different triangles?
You have acute, right, and obtuse triangles when referring to the measure of the largest angle, and you have equilateral, isosceles, and scalene triangles when referring to the congruency of the triangle's sides.
What is the point where all three angle bisectors of a triangle intersect?
Its technical name is the incenter; it's also the center of the largest circle that can be inscribed within the triangle. (It is also equidistant from the nearest point along each of the three sides, if that's not obvious.)
Find the dimensions of the rectangle of largest area that can be inscribed in a circle of radius a?
The largest rectangle would be a square. If the circle has radius a, the diameter is 2a. This diameter would also be the diameter of a square of side length b. Using the Pythagorean theorem, b2 + b2 = (2a)2. 2b2 = 4a2 b2 = 2a2 b = √(2a2) or a√2 = the length of the sides of the square The area of a square of side length b is therefore (√(2a2))2 = 2a2 which is the largest area for a rectangle inscribed in a circle of radius a.
What is the largest angle of a triangle with sides of 5.8 cm 14.1 cm and 8.3 cm?
The given dimensions will not form any kind of triangle because the sum of its 2 smallest sides is equal to its longest side and so therefore finding the largest angle is not possible.
What is the classification of the triangle?
A triangle can be classified according to its sides or the magnitude of its largest angle (two of the angles MUST be acute angles). All three sides equal: equilateral. Such a triangle must be equiangular, but that term is rarely used. Two equal angles, third one different (or two sides equal and third different): isosceles. All three angles different (all three sides different): scalene. Largest angle = 90 degrees: A right angled triangle. Largest angle obtuse: An obtuse angled triangle.
