2010 · Q79
In the figure given above, AS is a line of length 2a, with M as mid- point. Semicircles are drawn on one side with AM, MB and AB as diameters. A circle with centre O and radius r is drawn such that this circle touches all the three semicircles. What is the value of r ?
[Figure: see official question paper]
Elementary MathematicsMensuration
- A2a/3
- Ba/2
- Ca/3
- Da/ 4
Explanation
Soddy-type: (a/2)²+(a-r)²=(a/2+r)² gives r=a/3.