Abhijeet, T, S and R are “the points at which each angle bisector intersects the opposite side”. However, that is not the same as “the point of tangency of the side with the incircle”. The latter would be found, after obtaining the incentre (point Q above), by dropping perpendiculars from Q to each of the three sides.

Guess the diagram is a bit confusing..
Eagerly waiting for more theorems and problems on circumcentre and incentre, altitudes and median. Always been a pain for me!

I’ve explained in brief in the earlier reply. If you wish to understand more precisely, note that (a) the sides of the triangle are tangents to the incircle (b) the radius is perpendicular to the tangent at the point of contact and (c) the lines drawn here are angle bisectors and not perpendiculars. (You will have to figure out the rest for yourself)

i did not get the last point i.e. QT, QS and QR are not inradii.

Can you please explain what exactly you mean by that?

OK got it thanks!!!

can u also explain me why they r not inradii

Abhijeet, T, S and R are “the points at which each angle bisector intersects the opposite side”. However, that is not the same as “the point of tangency of the side with the incircle”. The latter would be found, after obtaining the incentre (point Q above), by dropping perpendiculars from Q to each of the three sides.

regards

J

Guess the diagram is a bit confusing..

Eagerly waiting for more theorems and problems on circumcentre and incentre, altitudes and median. Always been a pain for me!

sir plzz tell me why QT, QS, QR r not inradii

I’ve explained in brief in the earlier reply. If you wish to understand more precisely, note that (a) the sides of the triangle are tangents to the incircle (b) the radius is perpendicular to the tangent at the point of contact and (c) the lines drawn here are angle bisectors and not perpendiculars. (You will have to figure out the rest for yourself)

regards

J