MathDB
Broken Line Path

Source:

June 13, 2009

Problem Statement

Diameter AB‾ \overline{AB} of a circle with center O O is 10 10 units. C C is a point 4 4 units from A A, and on AB‾ \overline{AB}. D D is a point 4 4 units from B B, and on AB‾ \overline{AB}. P P is any point on the circle. Then the broken-line path from C C to P P to D D: <spanclass=′latex−bold′>(A)</span> has the same length for all positions of P<spanclass=′latex−bold′>(B)</span> exceeds 10 units for all positions of P<spanclass=′latex−bold′>(C)</span> cannot exceed 10 units<spanclass=′latex−bold′>(D)</span> is shortest when △CPD is a right triangle<spanclass=′latex−bold′>(E)</span> is longest when P is equidistant from C and D. <span class='latex-bold'>(A)</span>\ \text{has the same length for all positions of }{P}\qquad\\ <span class='latex-bold'>(B)</span>\ \text{exceeds }{10}\text{ units for all positions of }{P}\qquad \\ <span class='latex-bold'>(C)</span>\ \text{cannot exceed }{10}\text{ units}\qquad \\ <span class='latex-bold'>(D)</span>\ \text{is shortest when }{\triangle CPD}\text{ is a right triangle}\qquad \\ <span class='latex-bold'>(E)</span>\ \text{is longest when }{P}\text{ is equidistant from }{C}\text{ and }{D}.
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