[tex]\text{Desenul este in fisierul atasat,}\\\\
\text{In trapezul ABCD desemnam segmentele:}\\
MC,~MB,~CP\perp AB,~P\in AB.\\\\
\text{In }\Delta BCP~\text{avem:}\\
PB=AB-CD=20-8=12~cm\\
CP=AD=16~cm\\
\Rightarrow~BC=\sqrt{PB^2+CP^2}=\sqrt{12^2+16^2}= \sqrt{144+256}= \sqrt{400}=\boxed{20cm}\\\\
\text{In }\Delta CDM~\text{avem:}\\
MD=6~cm\\
CD=8~cm\\
\Rightarrow~MC=\sqrt{MD^2+CD^2}=\sqrt{6^2+8^2}=\sqrt{36+64}= \sqrt{100}=\boxed{10~cm}\\\\
\text{In }\Delta ABM~\text{avem:}\\
AM=AD-MD=16-6=\boxed{10~cm}[/tex]
[tex]\text{In triunghiurile }\Delta MBA \text{ si }\Delta MBC \text{ avem:}\\\\
MA = MC = 10~cm\\
BA = BC = 20~cm\\
MB = \text{latura comuna}\\\\
\Longrightarrow~\text{Suntem in cazul LLL de congruenta.}\\\\
\Longrightarrow~ \Delta MBA \equiv \Delta MBC\\\\
\Longrightarrow~m(\sphericalangle MCB) = m(\sphericalangle MAB) = \boxed{90^o}[/tex]
