Mathematics, 04.04.2020 22:03 brianamarialove15
Acute △ABC with angles α, β, and γ is inscribed in a circle. Tangents to the circle at points A, B, and C intersect in points M, N, and P. Find measures of angles of the △MNP.
Answers: 1
![\gamma=\frac{1}{2}[arc\ AB] ---- arc\ AB=2\gamma\\\alpha=\frac{1}{2}[arc\ BC] ---- arc\ BC=2\alpha\\\beta=\frac{1}{2}[arc\ AC] ---- arc\ AC=2\beta](/tpl/images/0582/9240/38797.png)
![M=\frac{1}{2}[arc\ AB+arc\ BC-arc\ AC]](/tpl/images/0582/9240/bfd43.png)
![M=\frac{1}{2}[2\gamma+2\alpha-2\beta]\\M=[\gamma+\alpha-\beta]](/tpl/images/0582/9240/290ec.png)
![N=\frac{1}{2}[arc\ AC+arc\ BC-arc\ AB]](/tpl/images/0582/9240/a259f.png)
![N=\frac{1}{2}[2\beta+2\alpha-2\gamma]\\N=[\beta+\alpha-\gamma]](/tpl/images/0582/9240/4066e.png)
![P=\frac{1}{2}[arc\ AC+arc\ AB-arc\ BC]](/tpl/images/0582/9240/e426d.png)
![P=\frac{1}{2}[2\beta+2\gamma-2\alpha]\\P=[\beta+\gamma-\alpha]](/tpl/images/0582/9240/b0535.png)
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Acute △ABC with angles α, β, and γ is inscribed in a circle. Tangents to the circle at points A, B,...
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