Table of Contents
What is the formula of circumradius of a triangle?
The formula for the circumradius of a triangle with sides of lengths a, b, and c is (abc) / sqrt((a + b + c)(b + c – a)(c + a – b)(a + b – c)), and for a regular polygon with n sides of length s, it is s / (2sin(π / n)).
What is meant by circumradius?
: the radius of a circumscribed circle.
What is circumradius and Inradius?
Inradius The inradius( r ) of a regular triangle( ABC ) is the radius of the incircle (having center as l), which is the largest circle that will fit inside the triangle. Circumradius: The circumradius( R ) of a triangle is the radius of the circumscribed circle (having center as O) of that triangle.
What is circumradius of cube?
Description. A circumscribed sphere of a polyhedron is a sphere that contains the polyhedron and touches each of the polyhedron’s vertices. The radius of sphere circumscribed around a cube is called the circumradius.
What is circumradius of equilateral triangle?
Circumradius (R) Circumradius is defined as the radius of that circle which circumscribes (surrounds) the triangle. As shown in the above figure, the circle with centre O passes through the three vertices of the triangle ABC. NOTE: The ratio of circumradius to inradius in an equilateral triangle is 2:1 or (R = 2r).
How do you draw a triangle of circumradius 3cm?
Draw a triangle o
- 1) First draw a line CD. At C and with a protractor make an angle of 110° , as shown,
- 2) With C as the centre and a radius of 3 cm cut the line CE.
- 3) At B, and with a protractor, make an angle of 75° with BC, as shown below:
- 4) The other angles can be measured with the help of the protactor.
What is the difference between circumradius and radius?
As nouns the difference between radius and circumradius is that radius is (anatomy) the long bone in the forearm, on the side of the thumb while circumradius is (mathematics) for a given geometric shape, the radius of the smallest circle or sphere into which it will fit.
How do you construct the circumradius triangle 4cm?
With B as centre and radius of 4cm, draw an arc. Similarly, with C as centre and radius of 4cm, draw another arc to intersect the previous arc at A. Join AB and AC. ABC is the required equilateral triangle.
How do you draw a triangle with circumradius 3cm?
What is the circum radius of a right angled triangle?
Therefore, the given triangle is a right angled triangle. In a right-angled triangle, the circum radius measures half the hypotenuse. Additional Property: The median to the hypotenuse will also be equal to half the hypotenuse and will measure the same as the circumradius. The correct answer is Choice (2).
How is the center of a triangle related to the circumcircle?
In the case of a right triangle, the hypotenuse is a diameter of the circumcircle, and its center is exactly at the midpoint of the hypotenuse. This is the same situation as Thales Theorem, where the diameter subtends a right angle to any point on a circle’s circumference.
How is the radius of a triangle related to its hypotenuse?
The radius of the circumcircle is also called the triangle’s circumradius. In the case of a right triangle, the hypotenuse is a diameter of the circumcircle, and its center is exactly at the midpoint of the hypotenuse. This is the same situation as Thales Theorem, where the diameter subtends a right angle to any point on a circle’s circumference.
What is the circumradius of a cyclic polygon?
The circumradius of a cyclic polygon is the radius of the circumscribed circle of that polygon. For a triangle, it is the measure of the radius of the circle that circumscribes the triangle.