The solution to the geometry question on in-radius is given below. The question can be found here . This is a reasonably tough question and quite possibly in the higher end of difficulty level of questions that appear in the CAT.

One of our students has provided another solution for this using trigonometry as well. If you can get that solution, drop a comment. I will be more than happy to add that also on to the blog.

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Hi Rajesh

There is no need to calculate area to find the value of 'k'.

As per your diagram, I am taking the values as AB = AC = kr and BC = 3r.

We know that Incenter of a triangle is intersection point of angle bisectors of the triangle. So applying internal angle bisector theorem in triangle ACD, we have

AI = 2kr/3.

Now applying Pythagoras theorem in triangle ACD we can easily find the value k ad then the required ratio as follows:

(2kr/3 + r)^2 + (3r/2)^2 = (kr)^2.

I believe this is much faster, shorter and easier than the method presented in slideshare.

Rgds

Kamal Lohia