Prove  that the radius of the circle will be the length of the perpendicular from O on any side. (Triangle and incircle )

Asked by sucharitasahoo1 | 11th Oct, 2017, 08:44: PM

Expert Answer:

 
begin mathsize 16px style Let space ABC space be space straight a space triangle.
Draw space angle space bisectors space of space any space two space angles comma space say space angle straight B space and space angle straight C.
Suppose space they space intersect space at space straight I.
Then comma space as space straight I space lies space on space the space angle space bisectors space of space angle straight B space and space angle straight C comma space straight a space circle space can space be space drawn space with
centre space straight O space to space touch space AB comma space BC space and space AC comma
The space radius space of space the space circle space will space be space the space length space of space the space perpendicular space from space straight I space on space any space side.
This space circle space is space called space the space incircle space of space triangle ABC space and space its space centre space is space called space the space incentre space of space triangle ABC. end style

Answered by Rashmi Khot | 20th Dec, 2017, 05:04: PM