April 24, 2010

1. You are given an arc of a circle, how will you complete it to a full circle?
2. You are given three distinct points on a sheet of paper, label them A , B and C. How will you find a point D that minimizes the maximum distance to the points A, B and C? (Learn More: Fermat-Weber Geometric Medians)
   
3. Given three points on a sheet of paper, how will you draw a circle passing through those three points?
   
4. Let A be a point outside a circle centered at O. Draw a tangent to the circle. There are two tangents - consider just one of them. Let the tangent be incident to the circle at point B. Show (i.e., how to prove) that OB is perpendicular (i.e., makes an angle of 90 degrees) to AB.