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Line and tangent circle

Source: 1978 AHSME Problem 11

June 6, 2014
calculusderivativeanalytic geometrygraphing linesslopeAMC

Problem Statement

If rr is positive and the line whose equation is x+y=rx + y = r is tangen to the circle whose equation is x2+y2=rx^2 + y ^2 = r, then rr equals
<spanclass=latexbold>(A)</span>12<spanclass=latexbold>(B)</span>1<spanclass=latexbold>(C)</span>2<spanclass=latexbold>(D)</span>2<spanclass=latexbold>(E)</span>22<span class='latex-bold'>(A) </span>\frac{1}{2}\qquad<span class='latex-bold'>(B) </span>1\qquad<span class='latex-bold'>(C) </span>2\qquad<span class='latex-bold'>(D) </span>\sqrt{2}\qquad <span class='latex-bold'>(E) </span>2\sqrt{2}