Difference between revisions of "1975 AHSME Problems/Problem 11"

(Created page with "==Problem== Let <math>P</math> be an interior point of circle <math>K</math> other than the center of <math>K</math>. Form all chords of <math>K</math> which pass through <mat...")
 
Line 9: Line 9:
 
\textbf{(E)} \text{ a circle}
 
\textbf{(E)} \text{ a circle}
 
</math>
 
</math>
 +
 +
==Solution==
 +
 +
==See Also==
 +
{{AHSME box|year=1975|num-b=1|num-a=3}}
 +
{{MAA Notice}}

Revision as of 17:09, 19 January 2021

Problem

Let $P$ be an interior point of circle $K$ other than the center of $K$. Form all chords of $K$ which pass through $P$, and determine their midpoints. The locus of these midpoints is

$\textbf{(A)} \text{ a circle with one point deleted} \qquad \\ \textbf{(B)} \text{ a circle if the distance from } P \text{ to the center of } K \text{ is less than one half the radius of } K; \\ \text{otherwise a circular arc of less than } 360^{\circ} \qquad \\ \textbf{(C)} \text{ a semicircle with one point deleted} \qquad \\ \textbf{(D)} \text{ a semicircle} \qquad  \textbf{(E)} \text{ a circle}$

Solution

See Also

1975 AHSME (ProblemsAnswer KeyResources)
Preceded by
Problem 1
Followed by
Problem 3
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
All AHSME Problems and Solutions

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

Invalid username
Login to AoPS