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# What is the radius of the circumscribed circle of a right triangle?

## What is the radius of the circumscribed circle of a right triangle?

The hypotenuse of the triangle is the diameter of its circumcircle, and the circumcenter is its midpoint, so the circumradius is equal to half of the hypotenuse of the right triangle.

### What is the formula of radius of circumcircle?

Circumcircle of a triangle, radius = 4×s(s−a)(s−b)(s−c) abc.

#### How do you find the center of a circumscribed circle of a triangle?

When a circle circumscribes a triangle, the triangle is inside the circle and the triangle touches the circle with each vertex. find the midpoint of each side. Find the perpendicular bisector through each midpoint. The point where the perpendicular bisectors intersect is the center of the circle.

What is the radius of a circle inscribed in a triangle with sides of 12cm 35cm and 37cm?

We have to find the radius of inscribed circle in a triangle with sides of length 12cm , 35 cm and 37 cm. solution : see diagram, let O is the centre of inscribed circle in a triangle ∆ABC. Therefore the radius of circle is 5cm.

What is the radius of the circumscribed circle of △ ABC?

For any triangle △ABC, let s = 12 (a+b+c). Then the radius r of its inscribed circle is r=Ks=√s(s−a)(s−b)(s−c)s. Recall from geometry how to bisect an angle: use a compass centered at the vertex to draw an arc that intersects the sides of the angle at two points.

## What is the radius of circle inscribed in a triangle with sides 3cm 4cm and 5cm?

Therefore, radius of the circle is 6 cm.

### How do you find the radius of an inscribed circle in an equilateral triangle?

Formula to find the radius of the inscribed circle = area of the triangle / semi-perimeter of triangle.

#### How do you find the circumference of a circle with a triangle?

If a right triangle is inscribed inside a circle, then the arc intercepted by the right angle is a semicircle, making the hypotenuse of triangle a diameter. This is the diameter, also, so the circumference is \displaystyle C = \pi d = 30 \pi.

What is the radius of the inscribed circle?

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 the radius of a circle inscribed in a triangle with sides of length 12cm 35cm and 37cm?

## How do you find the equation of a circle inscribed in a triangle?

Given A, B, and C as the sides of the triangle and A as the area, the formula for the radius of a circle circumscribing a triangle is r = ABC / 4A and for a circle inscribed in a triangle is r = A / S where S = (A + B + C) / 2.

### What is the radius of the circle inscribed in an equilateral triangle ABC of side?

Construction:Join O and A, O and B, and O and C. Assume the radius of the circle as r cm. ⇒( 1/2× AB × OR) + (1/2× BC × OP) + (1/2× AC × OQ) = √3/4× (side)2. Hence, the radius of the inscribed circle is 3.46 cm.