## Determine the rectangle's area (Semi-circle and rectangle)

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### Solution

Using

**Pythagoras**theorem in the triangle \(\triangle MAB\), we get \[\begin{array}{r} (r+x)^{2}+y^{2}=6^{2} \\ =36 \\ r^{2}+2 r x+x^{2}+y^{2}=36 \end{array}\] \(x^{2}+y^{2}=r^{2} \) : Circle equation at the point \(M \), thus \[\begin{array}{r} r^{2}+2 r x+r^{2}=36 \\ 2r^{2}+2rx=36 \\ r^{2}+rx=18 \\ r(r+x)=18 \\ \Rightarrow BC\cdot AB=18 \end{array}\]
Home -> Solved problems -> Calculate the rectangle’s area

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Why does the number \(98\) disappear when writing the decimal expansion of \(\frac{1}{9801}\) ?

Home -> Solved problems -> Calculate the rectangle’s area