What is the ratio area of equilateral triangle and inscribed circle?

The area of the inscribed circle is pi*r^2 = pi. The area of the circumscribed circle is 4*pi*r^2 = 4*pi. The area of the triangle (height 3*r) = 3*sqrt(3)*r^2 = 3*sqrt(3).

How do you find the ratio of an equilateral triangle?

All sides in an equilateral triangle are equal, so we need to find the value of just one side to know the values of all sides. The height of an equilateral triangle divides it into two equal 30:60:90 triangles, which will have side ratios of 1:2:√3.

What is the ratio of the areas of circles inscribed and circumscribed in an equilateral triangle of side 12 cm?

Thus the required ratio is 4:1.

What is the ratio of triangle in circle?

Ratio of areas of triangles = 6nr : 3nr 2 = 4:1. 2. h is the radius of the inscribed circle. h = r 2 .

What is the length of an equilateral triangle inscribed in the circle?

Total length BC= BD+DC. BC=2×3√3=6√3cm. Note: If the question was given for isosceles triangle instead of equilateral triangle, the OA≠OB≠OC ≠radius.

What is the ratio of three angles of an equilateral triangle?

A fundamental theorem of geometry is that the angles in a triangle add up to 180 degrees (Pi radians). Given that the angles of an equilateral triangle are all equal, we find that all angles have a measure of 180/3 = 60 degrees (Pi/3 radians).

What is the ratio of a right triangle?

45°–45°–90° triangle The sides in this triangle are in the ratio 1 : 1 : √2, which follows immediately from the Pythagorean theorem. Of all right triangles, the 45°–45°–90° degree triangle has the smallest ratio of the hypotenuse to the sum of the legs, namely √22.

How to construct an equilateral triangle inscribed in a given circle?

How to construct (draw) an equilateral triangle inscribed in a given circle with a compass and straightedge or ruler. This is the largest equilateral that will fit in the circle, with each vertex touching the circle. This is very similar to the construction of an inscribed hexagon, except we use every other vertex instead of all six.

How do you find the radius of an inscribed circle?

So centroid O divides each median in the ratio 2:1 Note: so if each side of equilateral triangle is 5 unit, radius of the inscribed circle = 5√3/6 unit. If each side is 4 unit, radius = 4√3/6 unit …….

What is the ratio of the small circle to the big circle?

I am asked to find the ratio of the area of the small circle to the big circle. Let “s” be the area of the small circle and “b” for the big circle. Ratio = Area of small circle / Area of big circle = $\\frac{s}{b}$ The radius of the big circle is twice the radius of the small circle, so $R = 2r.$

What is the area of the circumscribed circle of a triangle?

The area of the circumscribed circle is 4*pi*r^2 = 4*pi. The area of the triangle (height 3*r) = 3*sqrt (3)*r^2 = 3*sqrt (3). You should be able to figure out the ratios from there. For an equilateral triangle, the angle bisectors , the medians and the perpendiculars dropped from a vertex onto the opposite side, coincide.