# 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?**

**Options:**

**Solution:**

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 (A_{R}) will be = area of triangle OAB + area of triangle OBC

Since, both are equilateral triangle, the area will be

Now, area of circle* ***A _{c} **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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