Question

All the vertices of a rhombus lie on a circle of radius R. If the length of one diagonal of the rhombus is D, then the area of the rhombus is:

• A. RD
• B. \(\frac{RD}{2}\)
• C. \(\sqrt{2} \cdot RD\)
• D. \(\frac{\sqrt{2} \cdot RD}{2}\)

Answer 1

The Correct Option is B

In a rhombus inscribed in a circle, the diagonals are equal in length and are diameters of the circle.
Therefore, the length of the other diagonal is also D.
\(\text{Area of a rhombus} = \frac{\text{diagonal}_1 \times \text{diagonal}_2}{2}\)

In this case, \(\text{Area} = \frac{D \times D}{2} = \frac{D^2}{2}\)

So, the area of the rhombus is \(\frac{D^2}{2}\)

Hence, the correct answer is (b) \(\frac{RD}{2}\)