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LPower of a point time

Source: 1959 AHSME Problem 32

August 14, 2013

geometrypower of a pointAMCcircleAMC 12

Problem Statement

The length

l

of a tangent, drawn from a point

A

to a circle, is

\frac43

of the radius

r

. The (shortest) distance from

A

to the circle is:

<span class='latex-bold'>(A)</span>\ \frac{1}{2}r \qquad<span class='latex-bold'>(B)</span>\ r\qquad<span class='latex-bold'>(C)</span>\ \frac{1}{2}l\qquad<span class='latex-bold'>(D)</span>\ \frac23l \qquad<span class='latex-bold'>(E)</span>\ \text{a value between r and l.}

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