Answer:
The product of CM and MB is;
[tex]853.45[/tex]
Explanation:
Given that the length of each sides of the equilateral triangle is
[tex]50.6[/tex]
So, the length CB equals 50.6.
Since AD is a bisector then the length CD would be;
[tex]\begin{gathered} CD=\frac{CB}{2}=\frac{50.6}{2} \\ CD=25.3 \end{gathered}[/tex]
Also, the triangle CDM formed by the bisectors is a right angled triangle.
Since line CE bisect angle ACB.
[tex]\begin{gathered} \measuredangle ACB=60^0\text{ (equilateral triangle)} \\ \measuredangle\text{DCM}=\frac{\measuredangle ACB}{2}=\frac{60^0}{2}=30^0 \end{gathered}[/tex]
We can then calculate the length of line MB and CM;
[tex]\begin{gathered} \cos (\measuredangle DCM)=\frac{CD}{CM} \\ \cos 30^0=\frac{25.3}{CM} \\ CM=\frac{25.3}{\cos 30^0} \\ CM=29.2139 \end{gathered}[/tex]
And since it is an equilateral triangle;
[tex]CM=MB=29.2139[/tex]
So;
[tex]\begin{gathered} CM\times MB=29.2139\times29.2139 \\ =853.45 \end{gathered}[/tex]
Therefore, the product of CM and MB is;
[tex]853.45[/tex]
