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In the diagram, diameter AC¯¯¯¯¯ intersects chord BD¯¯¯¯¯ at point E such that AE = 2.5 units and BE = 3.4 units. Point O is the center of the circle, and the radius of the circle is 5 units. What is the approximate length of DE¯¯¯¯¯?
By using the intersecting chord theorem, we can solve for the length of the line segment DE. The theorem states that for an intersecting chord AB and CD the lengths A×B is always equal to C×D no matter where the chords are. Calculation is as follows:
AE x CE = DE x BE 2.5 x 7.5 = DE x 3.4 DE = 5.5 units
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