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Question 1 of 2
A triangle is drawn with its vertices on the circle \( C \) such that one of its sides is a diameter of \( C \) and the other two sides have their lengths in the ratio \( a : b \). If the radius of the circle is \( r \), then the area of the triangle is:
In a rectangle \( ABCD \), \( AB = 9 \) cm and \( BC = 6 \) cm. \( P \) and \( Q \) are two points on \( BC \) such that the areas of the figures \( ABP, APQ, \) and \( AQCD \) are in geometric progression. If the area of the figure \( AQCD \) is four times the area of triangle \( ABP \), then \( BP : PQ : QC \) is: