Test your mathematical prowess
Q. Which of the following objects shown below are identical to the circled object?
 Answer
Q. Let ABC be a triangle with angle BAC= 60 degrees. Let AP bisect angle BAC and let BQ bisect angle ABC, with P on BC and Q on AC. If AB + BP = AQ +QB, what are the angles of the triangle?
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Q. Twenty-one girls and twenty-one boys took part in a mathematical competition. It turned out that (a) each contestant solved at most six problems, and (b) for each pair of a girl and a boy, there was at least one problem that was solved by both the girl and the boy. Prove that there was a problem that was solved by at least three girls and at least three boys.
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Q. In acute triangle ABC with circumcenter O and altitude AP, angle C is greater than or equal to angle B plus 30 degrees. Prove that angle A plus angle COP is less than 90 degrees.
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