ΔABC jest równoramienny gdzie I AC I = I BC I
[tex]\mid \measuredangle CAD \mid = \mid \measuredangle DAB\mid = \alpha \\\\\mid \measuredangle BAC\mid =2\alpha \\\\\dfrac{1}{2} \mid \measuredangle BAC\mid = \mid \measuredangle CAD \mid = \mid \measuredangle DAB\mid = \alpha\\\\\mid \measuredangle ADB \mid = 2\alpha\\\\[/tex]
[tex]\Delta ABC ~~i~~\Delta ABD~~sa~~podobne~~oraz~~\Delta ABC~~jest~~rownoramienny~~\Rightarrow[/tex]
[tex]\Rightarrow~~\Delta ABD ~~jest~~rownoramienny[/tex]
[tex]\mid AB \mid = \mid AD\mid ~~\land ~~\mid \measuredangle ABD \mid =\mid \measuredangle ADB \mid \\\\\mid \measuredangle ABD \mid =\mid \measuredangle ADB \mid =2\alpha ~~\land~~\mid \measuredangle DAB \mid =\alpha \\\\\alpha +2\alpha +2\alpha =180^{o} \\\\5\alpha =180^{o} ~~\mid \div~~5\\\\\alpha =36^{o} \\\\\mid \measuredangle BAC \mid =?\\\\\mid \measuredangle BAC \mid =2\alpha ~~\land ~~\alpha =36^{o} ~~\Rightarrow~~\mid \measuredangle BAC \mid=72^{o}[/tex]
Odp: Miara kąta BAC wynosi 72°.
