Inradius, Exradii and Circumradius
Inradius, Exradii and Circumradius: Overview
This topic covers concepts, such as, Circles Associated with a Triangle, Circum-circle of a Triangle, Circum-radius of a Regular Polygon & In-radius of a Regular Polygon etc.
Important Questions on Inradius, Exradii and Circumradius
The value of is equal to: where denote sides of a and is a in-radius of and is a circum-radius of



In a triangle The ratio of the radius of the circumcircle to that of the incircle is:

Prove that in any , where is the circumradius, the inradius, and the angle bisectors of the triangle.

Divya inscribed a circle inside a regular pentagon, circumscribed a circle around the pentagon, and calculated the area of region between the two circles. Mansi did the same with a regular heptagon. The area of the regions calculated by Divya and Mansi are and , respectively. Each polygon had a side length of . Which of the following is true?

Let be triangle with . If the circum radius of the triangle is , then equals

Let be a nine-sided regular polygon with side length units. The difference between the lengths of the diagonals and equals

If is the circum radius of , then = ….

The value of is equal to: where denote sides of a and is a in-radius of and is a circum-radius of

In , BC = 13 cm, AC = 14 cm and AB = 15 cm, then its circum-radius is equal to

are internal angular bisectors of and is the incentre. If then the value of is:

Let be the orthocentre of triangle Then the angle subtended by side at the centre of incircle of is:

If r1 = 8, r2 = 12, r3 = 24, then r is equal to

In a triangle , then the triangle is ( r1, r2 and r3 are exradii of traingle)

In any the line joining the circumcentre and incentre is parallel to then is equal to-

Find the area of the circumcircle of , if .

In a triangle, if .Tick the appropriate option.

Let and be the side lengths of a triangle and assume that and If then find the minimum value of where and denote inradius and circumradius of triangle

If , then prove that the triangle is right-angled.
