1957 AHSME Problems/Problem 34

Problem

The points that satisfy the system $x + y = 1,\, x^2 + y^2 < 25$ , constitute the following set:

$\textbf{(A)}\ \text{only two points} \qquad \\ \textbf{(B)}\ \text{an arc of a circle}\qquad \\ \textbf{(C)}\ \text{a straight line segment not including the end-points}\qquad\\ \textbf{(D)}\ \text{a straight line segment including the end-points}\qquad\\ \textbf{(E)}\ \text{a single point}$

Solution

$[asy] import geometry; // Axes draw((0,-8)--(0,8),arrow=Arrows); label("$y$",(0,9)); draw((-8,0)--(8,0),arrow=Arrows); label("$x$",(9,0)); // Circle and Line draw(circle((0,0),5),red+dashed); draw(line((0,1),(1,0)),blue); [/asy]$

$\fbox{\textbf{(C)} a straight line segment not including the end-points}$ .

1957 AHSC (Problems • Answer Key • Resources)
Preceded by Problem 33	Followed by Problem 35
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 • 26 • 27 • 28 • 29 • 30 • 31 • 32 • 33 • 34 • 35 • 36 • 37 • 38 • 39 • 40 • 41 • 42 • 43 • 44 • 45 • 46 • 47 • 48 • 49 • 50
All AHSME Problems and Solutions

The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.

Page

Toolbox

Search

1957 AHSME Problems/Problem 34

Problem

Solution

See Also