Question: AB and CD are chords of a circle intersecting at P. If AP \times PB = 48 square units, then what is CP \times PD equal to? Statement I: AP = 8 units Statement II: CP = 10 units

A Question is given followed by two Statements I and II. Consider the Question and the Statements. Which one of the following is correct in respect of the above Question and the Statements?

  1. A. The Question can be answered by using one of the Statements alone, but cannot be answered using the other Statement alone
  2. B. The Question can be answered by using either Statement alone
  3. C. The Question can be answered by using both the Statements together, but cannot be answered using either Statement alone
  4. D. The Question can be answered even without using any of the Statements ✓

Correct Answer: D. The Question can be answered even without using any of the Statements

Explanation

By the intersecting chords theorem, AP \times PB = CP \times PD. Since AP \times PB is given as 48, CP \times PD must also equal 48. The answer is found directly without using either statement.

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