In RD Sharma Chapter 15 : Areas related to circles: Revision exercise Question 32, how is the radius of the circle with centre C ,1/6th of AB ..???
Hey, actually at first I also had the same problem, but later on I found out the answer. You need to do some sort of constructions in that ques.
1. Join C with the centres of any of the semi-circles drawn on AM MB and then join CM.
Now, CM is the tangent to semi-circle AM or MB
Let the centre of semi-circle AM be X.
So, In triangle CMX,
= (CX)2 = (CM)2 + (MX)2
= (9+r)2 = (18-r)2 + (9)2 ( let radius of circle with cantre C be 'r' )
= On simplifying,
r = 6cm = AB/6.