Math CentralQuandaries & Queries


Question from Kameron:

I have been given a challenge problem that states that Diameter AB is drawn in a circle if 10 inch. Chords AC and BD are drawn so that each is of length 12inch and ACDB is a trapezoid. Find the height, in inches, of the trapezoid

Hi Kameron,

Can you check the wording of the question? I don't understand "if 10 inch". What does the ten inches measure?


It's the radius.


Hi Kameron,

I drew a diagram (not to scale). $P$ is the center of the circle and $DE$ is perpendicular to $$PB.$


$h = |DE|$ is the height of the trapezoid and it's also the height of the triangle $DPB$ with base $PB.$ The area $A$ of the triangle $DPB$ is given by

\[A = \frac12 |PB| \times h = 5 h.\]

If you could find the area of the triangle $DPB$ a different way then you would have $A = 5 h$ and you could solve for $h.$ Can you find the area of the triangle $DPB?$


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