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

The correct option is B Statement (I) alone is sufficient, but statement (II) alone is not sufficient.
Since, all three circles are equal.
PQ=QR=PR
ΔPQR is an equilateral triangle.
And area of shaded portion.
= Area of ΔPQR3 (area of each sector),
(I) QR is known.
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.

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