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Properties of Circles

What is pi? If the area of a circle is 49π, what is its circumference? If a circle is inscribed in a square, what is the ratio of the areas of the circle and the square?

Problem Solving

         

In the above diagram, \(d_1=24\) and \(d_2=18.\) What is the perimeter of the green colored region?

In the above image, \( \angle ABC = 115 ^ \circ \). What is angle \( AOC \) (as marked) equal to?

The length of each side in the above square is \(14.\) If the two curves in the square are each one quarter of a circle with radius \(14,\) calculate the area of the region bounded by the two curves in the above diagram.

\(\Gamma\) is a circle with center \(O\). \(A\) and \(B\) are points on \(\Gamma\) such that the sector \(AOB\) has perimeter \(80\). What is the maximal possible area of sector \(AOB\)?

Let \(O_1\) and \(O_2\) be the centers of two circles with the same radius \(15\text{ cm}.\) What is the perimeter of the green colored region?

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