What is the maximum area of triangle that can be inscribed in a circle?
equilateral triangle
Show that the triangle of maximum area that can be inscribed in a given circle is an equilateral triangle.
What is the area of largest triangle that can be inscribed in a circle of radius one unit?
2r2 sq. units.
What is the area of a triangle inscribed in a circle?
If you join the opposite vertices, you get 4 equal, right triangles with legs r and r. Hence area=4 x 1/2 x 5 x 5 =50 sq.cm. Originally Answered: What will be the area of an equilateral triangle inscribed in a circle with a radius of 5cm? 75√3/4=75×1.732/4=75×0.433=32.5sqcm.
What is the area of the largest triangle that can be inscribed in a circle with radius 12?
The area of the largest triangle that can be inscribed in a circle of radius 12 is 108*sqrt 3.
What is the area of a circle that can be inscribed in a square of side 6 cm?
36 πcm2.
What is the ratio of the areas of a circle and an equilateral triangle?
The Ratio of the Areas of circle and equilateral ∆ is π : √3 .
How do you find the radius of a circumscribed circle in a triangle?
For a triangle △ABC, let s = 12 (a+b+ c). Then the radius R of its circumscribed circle is R=abc4√s(s−a)(s−b)(s−c). In addition to a circumscribed circle, every triangle has an inscribed circle, i.e. a circle to which the sides of the triangle are tangent, as in Figure 12.
When the radius of a circle is doubled the area is multiplied by?
and pi is constant. Thus we can say that the the of a circle is directly proportional to the square of the radius of the circle. This means, if the radius of the circle is doubled, then the area of the circle will increase by 2^2 = 4 times, i.e. quadrupled.
What is the area of the incircle of a triangle?
The distances from the incenter to each side are equal to the inscribed circle’s radius. The area of the triangle is equal to 21 ×r× (the triangle’s perimeter), where r is the inscribed circle’s radius.
When is a triangle inscribed in a circle?
If a side of the triangle is 20root3 then the radius of the circle is A triangle of the maximum area is inscribed in a circle. If a side of the triangle is 20root3 then the radius of the circle is
What is the maximum area of an equilateral triangle?
The maximum area will be for an equilateral triangle. Draw a radial line from each vertex to the circle’s centre, to make three isosceles triangles. The central angle $θ$ is 120 degrees or 2π/3 radians. The area of each triangle is $\\frac {r^2\\sinθ}{2}$ and the whole area will be 3 times that.
Which is the maximum triangle in a circle?
This way you can show that the maximum triangle is (at least) isosceles. Now, the law of the sines states that a sinˆA = b sinˆB = 2R where R is the radius of the circumscribed circle, that is, 1.