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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
3 years, 9 months 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 $\dfrac{1}{2}-\dfrac{1}{5}=\boxed{\dfrac{3}{10}}$ · 3 years, 9 months ago

There is something special about triangle U. See if anyone else can figure it out. Hint: right triangle · 3 years, 9 months ago