## Problem Of The Week 17

**Two points are selected randomly on the surface of a sphere of radius R. What is the expected distance between them, along the surface of the sphere? **

Problem is simple if you think logically, else you will have issues. This question is taken from teh CAT quant Blog by Suresh, the link of which you can see on the right!

* Tipster*: The sum of the two legs of a right angled triangle is equal to sum of diameters of incircle and circumcircle🙂

we can easily take the two points to be lying on a cirle, and the rest of the sphere can be ignored. so the problem reduces to two points on the perimeter of a cirlce.

if the two points make an angle theta , then distance= 2*pi*r*theta /360.

ankitSeptember 19, 2008 at 12:52 pm

This is incorrect

outtimedSeptember 20, 2008 at 4:07 am

whtz the answer to this ques ????

crushkillerSeptember 20, 2008 at 6:37 am