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# geometry

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In triangle ABC ,  AB= AC=5 and BC=7. Let O be the circumcenter of triangle ABC. Find the area of triangle OBC .

May 20, 2022

#1
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Find the area of triangle OBC .

Hello Guest!

The triangle is symmetrical in the X-Y coordinate system with BC on the ordinate axis.

$$A(0,\sqrt{5^2-3.5^2})= A(0,\sqrt{12.75})\\ B(-3.5,\ 0)\\ C(3.5,\ 0)\\ M(\frac{7}{4},\frac{\sqrt{12.75}}{2})\ [center\ \overline{AC}]\\ m_{AC(x)}=-\frac{\sqrt{12.75} }{3.5}\\ m=\frac{3.5}{\sqrt{12.75}}$$

$$MO(x)=m_{}(x-x_M)+y_M\\ MO(x)=\frac{{3.5}}{\sqrt{12.75}}(x-\frac{7}{4})+\frac{3.5707}{2}\\ h=MO(0)=\frac{{3.5}}{\sqrt{12.75}}(0-\frac{7}{4})+\frac{\sqrt{12.75}}{2}\\ h=0.0700147\\ A_{OBC}=\dfrac{0,0700147\cdot 7}{2}\\ \color{blue}A_{OBC}=0.1225245\\ Finally\ solved!\\ (The\ circular\ function:\ f(x)=\sqrt{3.5^2+0.0700147^2-x^2}+0.0700147)$$

!

May 21, 2022
edited by asinus  May 21, 2022
edited by asinus  May 21, 2022
edited by asinus  May 22, 2022
edited by asinus  May 22, 2022
edited by asinus  May 23, 2022
edited by asinus  May 23, 2022
edited by asinus  May 23, 2022