1967 AHSME Problems/Problem 29

Problem

$\overline{AB}$ is a diameter of a circle. Tangents $\overline{AD}$ and $\overline{BC}$ are drawn so that $\overline{AC}$ and $\overline{BD}$ intersect in a point on the circle. If $\overline{AD}=a$ and $\overline{BC}=b$ , $a \not= b$ , the diameter of the circle is:

$\textbf{(A)}\ |a-b|\qquad \textbf{(B)}\ \frac{1}{2}(a+b)\qquad \textbf{(C)}\ \sqrt{ab} \qquad \textbf{(D)}\ \frac{ab}{a+b}\qquad \textbf{(E)}\ \frac{1}{2}\frac{ab}{a+b}$

Solution

$\fbox{C}$

1967 AHSC (Problems • Answer Key • Resources)
Preceded by Problem 28	Followed by Problem 30
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1967 AHSME Problems/Problem 29

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