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Womens health [Obs] [Gyn] QUESTION #8191
Question 1

In the circle below, AB is a diameter. Points C and D lie on the circle, with C and D on the same side. Compare:

A B C D

Quantity A: The length of AB

Quantity B: The arithmetic mean of the lengths of AC and AD

  • Quantity A is greater✔️
  • Quantity B is greater
  • The two quantities are equal
  • The relationship cannot be determined from the information given
Correct Answer Explanation

Since AB is a diameter, any chord of the circle has length at most equal to the diameter.

Both AC and AD are chords of the circle (from B to points on the circle), so $AC \leq AB$ and $AD \leq AB$.

Their average: $\dfrac{AC + AD}{2} \leq AB$.

Equality holds only if both C and D coincide with A, which is not possible since C and D are distinct points on the circle different from A.

Therefore $\dfrac{AC + AD}{2} < AB$, and Quantity A is greater.