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Help Me In Geometry Problem

Here, AD=BD , BM=CM. BC=\(1\).What is the area of the triangle which is marked with U

Note by Fazla Rabbi
4 years ago

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There are two D's in the problem, so let the D on AB be \(N\). Let \(O=DM\cap CN\).

We must find \[[DNO]=[DNC]-[DOC]\] Since the sidelength is 1, \([DNC]=\dfrac{1}{2}\). Since \(\triangle DNC\sim\triangle DCM\), \[\dfrac{[DNC]}{[DCM]}=\dfrac{DC^2}{DM^2}=\dfrac{1}{\dfrac{5}{4}}=\dfrac{4}{5}\] Also, \([DCM]=\dfrac{1}{4}\), so \([DOC]=\dfrac{1}{5}\). Therefore, the answer is \[\dfrac{1}{2}-\dfrac{1}{5}=\boxed{\dfrac{3}{10}}\]

Daniel Chiu - 4 years ago

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There is something special about triangle U. See if anyone else can figure it out. Hint: right triangle

Daniel Liu - 4 years ago

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Suryansh Tiwari - 3 years, 12 months ago

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