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1967 AMC 12 Question 29

AMC12 · 1967 AMC 12

Question 29

$AB$ is a diameter of a circle. Tangents $AD$ and $BC$ are drawn so that $AC$ and $BD$ intersect in a point on the circle. If $AD=a$ and $BC=b,$ $a\ne b,$ the diameter of the circle is:
  1. $\lvert a-b\rvert$
  2. $\dfrac12(a+b)$
  3. $\sqrt{ab}$
  4. $\dfrac{ab}{a+b}$
  5. $\dfrac12\cdot\dfrac{ab}{a+b}$