Home
Class 12
MATHS
If the distance between incenter and one...

If the distance between incenter and one of the excenter of an equilateral triangle is 4 units, then find the inradius of the triangle.

Text Solution

Verified by Experts

Distance between excenter `I_(1) and` incenter I is
`II_(1) = 4R sin.(A)/(2) = 4` (given)
Since triangle, we have
`4 = 4R sin.(pi)/(6)`
or `R = 2`
`:. R = 2r = 2`
or `r = 1`
Promotional Banner

Topper's Solved these Questions

  • PROPERTIES AND SOLUTIONS OF TRIANGLE

    CENGAGE|Exercise Exercise 5.1|12 Videos

  • PROPERTIES AND SOLUTIONS OF TRIANGLE

    CENGAGE|Exercise Exercise 5.2|8 Videos

  • PROGRESSION AND SERIES

    CENGAGE|Exercise ARCHIVES (MATRIX MATCH TYPE )|1 Videos

  • PROPERTIES OF TRIANGLE, HEIGHT AND DISTANCE

    CENGAGE|Exercise Question Bank|15 Videos

Similar Questions

Explore conceptually related problems

The perimeter of an equilateral triangle is 60 cm then the area of the triangle is . . . . . .

The perimeter of an equilateral triangle is 30 cm. The area is

Prove that the distance between the circumcenter and the incenter of triangle ABC is sqrt(R^2-2R r)

Prove that the distance between the circumcenter and the incenter of triangle ABC is sqrt(R^2-2R r)

Find the area of an equilateral triangle whose perimeter is 180 cm.

Show that the angles of an equilateral triangle are 60^@ each.