¶ 1964 AHSME Problem 39
Problem: The magnitudes of the sides of triangle are , and , as shown, with . Through interior point and the vertices lines are drawn meeting the opposite sides in , respectively. Let . Then, for all positions of point is less than:
Answer Choices:
A.
B.
C.
D.
E.
Solution:
The length of each of the lines through must be less than the length of the larger of the two sides of the triangle adjacent to the line through . To see this let BB' be fixed and allow point to take a position very close to . Then takes a position very close to so that is very nearly equal to , but less than . Similarly, ' remains smaller than a and remains smaller than a for all interior positions of P}.
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