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Difference between revisions of "1975 AHSME Problems/Problem 11"
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==Solution==
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==Solution 1==
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It is (E) a circle.
  
 
==See Also==
 
==See Also==
 
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Revision as of 11:10, 20 August 2025

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 1

It is (E) a circle.

See Also

1975 AHSME (Problems • Answer Key • Resources)
Preceded by
Problem 10 		Followed by
Problem 12
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

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