[tex]1. \: MC \: is \: tangent \: to \: (B)\Rightarrow \widehat{BCM}=90° \\ 2. \: MC \: and \: MZ \: are \: tangent \: to \: (B)\Rightarrow MC = MZ\Leftrightarrow 5x - 9 = x + 7\Leftrightarrow x = 4 \\ 3. \: BM = \sqrt{ {BC}^{2} + {MC}^{2} } = \sqrt{ {5}^{2} + {12}^{2} } = 13 \\ \Rightarrow EM = BM - BE = BM - BC = 13 - 5 = 8 \\ 4. \: \tan(60°) = \frac{MC}{BC} = \frac{13 \sqrt{3} }{ BC}\Leftrightarrow BC = \frac{13 \sqrt{3} }{\tan(60°)} = \frac{13 \sqrt{3} }{ \sqrt{3} } = 13 \\ 5. \: MC = \sqrt{ {BM}^{2} - {BC}^{2} } = \sqrt{ {20}^{2} - {12}^{2} } = 16 \\ 6. \:BZ = \sqrt{ {BM}^{2} - {MZ}^{2} } = \sqrt{ {25}^{2} - {20}^{2} } = 15 \\ \Rightarrow XE=BX+BE=BZ+BZ=15+15=30[/tex]
