Sage-Tips

How do you find the distance between the incenter and the circumcenter?

Hence it is proved that the distance between the circumcenter and the incenter of the triangle ABC is $\sqrt {{R^2} – 2Rr} $.

What is the relation between radius of circumcircle and hypotenuse of the triangle?

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What is the relationship between inradius and Circumradius?

NOTE: The ratio of circumradius to inradius in an equilateral triangle is 2:1 or (R = 2r).

What is the formula for Circumradius?

The circumradius of a polygon is the radius of its circumcircle. 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)).

How do you find the distance between the Incentre and the Circumcentre of a right angle triangle?

Answer Expert Verified

1. Find the inradius of the incircle of side 6, 8 & 10 : Find the semi-perimeter : s = 1/2 ( a + b + c ) = 1/2 ( 6 + 8 + 10 ) = 12.
2. To find circumradius: R = abc / 4 = 480 / 96 = 5 cm.
3. To find the difference between the circumcircle and incircle:

What is the distance between Incentre and centroid?

The distance from the incenter to the centroid is less than one third the length of the longest median of the triangle.

What is the ratio of the inradius and circumradius of a square?

1 : √2
Detailed Solution ∴ The ratio of the inradius and circumradius of a square is 1 : √2.

How do you find the area of a Circumcircle?

We know that area of circle = π*r2, where r is the radius of given circle. We also know that radius of Circumcircle of an equilateral triangle = (side of the equilateral triangle)/ √3. Therefore, area = π*r2 = π*a2/3.

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