MathDB
The circle and the x-axis

Source: 2017 AMC 12B #6

February 16, 2017
AMCAMC 122017 AMC 12Bcoordinategeometry

Problem Statement

The circle having (0,0)(0,0) and (8,6)(8,6) as the endpoints of a diameter intersects the xx-axis at a second point. What is the xx-coordinate of this point?
<spanclass=latexbold>(A)</span> 42<spanclass=latexbold>(B)</span> 6<spanclass=latexbold>(C)</span> 52<spanclass=latexbold>(D)</span> 8<spanclass=latexbold>(E)</span> 62<span class='latex-bold'>(A)</span>\ 4\sqrt2 \qquad <span class='latex-bold'>(B)</span>\ 6\qquad <span class='latex-bold'>(C)</span>\ 5\sqrt2 \qquad <span class='latex-bold'>(D)</span>\ 8 \qquad <span class='latex-bold'>(E)</span>\ 6\sqrt2