Multiple choice

A chord PQ of the circle C divides it into two segments such that 3 times the area of the major segment is 4 times the area of the minor segment. Question: What is the radius of C? Statement I: Area of the minor segment is 66 square cm. Statement II: Area of the major segment is 88 square cm.

  1. The Question can be answered by one of the Statements alone but not by the other.

  2. The Question can be answered by either Statement alone.

  3. The Question can be answered by using both the Statements together, but cannot be answered by using either Statement alone.

  4. The Question cannot be answered even by using both Statements together.
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The area of the circle is fixed. If we know the area of either the major or minor segment, we can determine the total area of the circle and thus the radius. Both statements provide sufficient information.

AI explanation

Statement I gives the minor segment area as 66, and using the given ratio the major segment area is (4/3) × 66 = 88. This means the total circle area is 66 + 88 = 154, which allows you to find the radius. Statement II provides the major segment area as 88, leading to the same calculations in reverse to find the total circle area of 154. Because either statement alone fixes the total area of the circle at 154 square centimeters, the radius can be determined from either one independently. The question can be answered by either Statement alone.

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