Math CentralQuandaries & Queries


Question from ANJANA:

AB is a diameter of a circle.
C is a point in AB such that CA = 9 cm and CB = 25 cm.
Find the length of the shortest chord through C.


The shortest chord through C is perpendicular to the diameter AB. (To prove this claim one needs to know that for any chord PQ through C, the product PC*CQ is constant. One then wants the smallest sum x+y over all x's and y's for which x*y is constant.) Use the Pythagorean theorem to find the length PC.


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