2015 · Q81
AB is a line segment of length 2a, with M as mid point. Semicircles are drawn on one side with AM, MB and AB as diameter as shown in the above figure. A circle.with centre O and radius r is drawn such that this circle touches all the three semicircles. The value of r is
Elementary MathematicsGeometry: Lines, Angles and Triangles
- A2a/3
- Ba/2
- Ca/3
- Da/4
Explanation
With M at the origin, the circle's centre (0, a - r) satisfies (a - r)^2 = r^2 + a*r (tangency to a small semicircle), giving a^2 = 3ar, i.e. r = a/3. Hence option (c).