QOTD - Quantitative Aptitude Problem - Mensuration
2019-08-22 | Team PendulumEdu
A rhombus is inscribed in a circle in such a way that one vertex of rhombus is on the center while other three vertices are on the circumference of the circle. If the radius of the circle is 4 m then, what will be the ratio of area of circle and rhombus?
According to the information given in the question, the schematic will be
In the above figure,
OA = OC = OB = radius of circle
Since, the opposite sides of a rhombus are equal
Thus, OA = CB and OC = AB
So, from the above figure,
Area of rhombus OABC (AR) will be = area of triangle OAB + area of triangle OBC
Since, both are equilateral triangle, the area will be
Now, area of circle Ac will be
Therefore, the ratio of the area of circle to that of rhombus will be
Hence, (D) is the correct answer.
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