How do you find the radius of a circle inscribed in a rhombus?

Also radius of the circle, r, inside a rhombus is = xy/2√(x^2+y^2). So, radius of the circle in terms of l & b is = lb/2√(l^2+b^2).

How do you find the area of an inscribed rhombus?

Circle inscribed in a rhombus touches its four side a four ends. The side of rhombus is a tangent to the circle. Here, r is the radius that is to be found using a and, the diagonals whose values are given. Now the area of triangle AOB = ½ * OA * OB = ½ * AB * r (both using formula ½*b*h).

How do you find the area of a rhombus with the diagonals?

The formula for the diagonal of a rhombus is derived using the area of the rhombus. In other words, if the area and one of the diagonals is given, then the other diagonal can be calculated using the formula, p = (2 × Area)/q, where ‘p’ and ‘q’ are the two diagonals of the rhombus.

How do you find the area of an inscribed circle?

When a circle is inscribed in a square, the length of each side of the square is equal to the diameter of the circle. That is, the diameter of the inscribed circle is 8 units and therefore the radius is 4 units. The area of a circle of radius r units is A=πr2 .

What is the radius of a circle inscribed in a rhombus with diagonals of length 12 and 16?

The radius of the circle is equal to the length of the perpendicular drawn on hypotenuse from opposite vertex = base x perpendicular ÷ hypotenuse. Here, length of perpendicular = radius of circle = 8 * 6/10 = 48/10. Area of circle = π (48/10)² and area of rhombus = product of diagonals/2 = 16*12/2 = 96.

Can a circle be inscribed in a rhombus?

A circle is inscribed in the quadrilateral with the centre of the circle right on the intersection point of the 2 diagonals. The circumference of the circle touches all 4 sides of the rhombus. The diagonals of a rhombus are perpendicular, so ABO is a right triangle with right angle at the center O.

What are rhombus diagonals?

Every rhombus has two diagonals connecting pairs of opposite vertices, and two pairs of parallel sides. The two diagonals of a rhombus are perpendicular; that is, a rhombus is an orthodiagonal quadrilateral. Its diagonals bisect opposite angles.

How do you find the square footage of a rhombus?

Rhombus: Area (ft2) = Base × Altitude. Sector: Area (ft2) = Pi × R2 × (θ / 360°)

How do you solve an inscribed circle?

By the inscribed angle theorem, the measure of an inscribed angle is half the measure of the intercepted arc. The measure of the central angle ∠POR of the intercepted arc ⌢PR is 90°. Therefore, m∠PQR=12m∠POR =12(90°) =45°.

How do you find the radius of an inscribed circle?

Here is a formula in terms of the three sides: If the sides have length a, b, c, we define the semiperimeter s to be half their sum, so s = (a+b+c)/2. Given this, the radius is given using the following: r2 = (s – a)*(s – b)*(s – c) / s.

What is special about a rhombus inscribed in a circle?

When a rhombus is inscribed in a circle, it’s two diagonals required to be the diameters of the circle. As the diameters of a circle is constant (2* radius) – rhombus inscribed in a circle must have equal diagonals , which is only possible when the said rhombus is a square only.

What are the properties of a rhombus?

Convex polygon
Isotoxal figure
Rhombus/Properties