Problema Solution
While digging for edible roots Megan has uncovered a portion of terra-cotta pipe. Alex believes this relic to be part of an early water drainage system. To determine the diameter of the original pipe, Megan lays a meter stick across the longest portion and measures the length of the chord at 46 cm. The depth of the portion from the midpoint of the chord is 6 cm. From these two measurements you set about finding the dimensions of the original pipe. What was the pipe's original diameter?
Answer provided by our tutors
We have a circle with center O.
Draw the chord AB, where AB = 48.
Draw radii OA and OB = R.
Draw radius OD perpendicular to AB, crossing at C. CD = 6, AC = CB = 48/2 = 24.
Since OD = R, then OC = R - 6
In right triangle OCB, OC^2 + BC^2 = OB^2
or: (R - 6)^2 + 24^2 = R^2
Hence, R = 51 cm.
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The diameter is: D = 2*R = 2*51 = 102 cm.