- Given a unit square, what is the ratio of the areas of two circles - the circle with maximum area lying completely inside the circle, and the area of the smallest area circle that completely encloses the square.
- How to do the same problem with a cube and inscribing and circumscribing sphere?
- Given a unit square, you want to place a triangle whose area is maximum that lies completely inside the square. What will be its area?
- How to do the same problem with a triangle in the cube?
- How many corns on a corn? Typically a corn is cube shaped measuring 4mm, and a corn cone is of diameter of 7cms and has a length of 27cms.
- Show that in a circle, if we take two chords of the same length, then the angle they form at the center of the circle is the same.
- Show that in a circle, the line joining the center of the circle to the mid point of any chord, is perpendicular to the chord.
- How many circles pass through a single point? Two points? What about three points? Show that if three points do not lie on a straight line, there is a unique circle passing through them.
- Show that the angle subtended by any arc of the circle at the center is double of the angle subtended by this arc at any point on the circle.
Sunday, June 26, 2011
Sunday, June 26, 2011
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