Question

In the given figure P, Q and R are centres of three equal circles. What is the area of the shaded portion in the figure shown below?
(I) QR is known.
(II) The triangle is an equilateral triangle.

• A. Statement (I) alone is sufficient, but statement (II) alone is not sufficient.
• B. Statement (II) alone is sufficient, but statement (I) alone is not sufficient.
• C. Both statements together are sufficient, but neither statement alone is sufficient.
• D. Each statement alone is sufficient.

Answer 1

Answer: (A)

Statement (I) alone is sufficient, but statement (II) alone is not sufficient.

Since, all three circles are equal.
$\therefore PQ=QR=PR$
$\Rightarrow \Delta PQR$ is an equilateral triangle.
And area of shaded portion.
$=$ Area of $\Delta PQR-3$ (area of each sector),
(I) $\Rightarrow QR$ is known.
$\Rightarrow$ side of triangle and radius is known.
Hence, statement (I) alone is sufficient to answer the question.
Now, since all three circles are equal, therefore, statement (II) is re-statement of the information given in question.