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Plane Trigonometry
 The Triangle and Circle
 Sources and References

Plane Trigonometry

The Triangle and Circle

Let π‘Ÿ = radius of inscribed circle π‘Ÿπ‘Ž = radius of eseribed circle touching the side π‘Ž 𝑅 = radius of circumscribing circle 709 image π‘Ÿ=△𝑠From Fig., β–³=π‘Ÿπ‘Ž2+π‘Ÿπ‘2+π‘Ÿπ‘2 710 π‘Ÿ=π‘Žsin𝐡2sin𝐢2cos𝐴2By π‘Ž=π‘Ÿcot𝐡2+π‘Ÿsin𝐢2 711 π‘Ÿπ‘Ž=β–³π‘ βˆ’π‘ŽBy β–³=π‘Ÿπ‘Žπ‘2+π‘Ÿπ‘Žπ‘2βˆ’π‘Ÿπ‘Žπ‘Ž2 712 π‘Ÿπ‘Ž=π‘Žcos𝐡2cos𝐢2cos𝐴2By π‘Ž=π‘Ÿπ‘Žtan𝐡2+π‘Ÿtan𝐢2 713 image 𝑅=π‘Ž2sin𝐴=π‘Žπ‘π‘4β–³By III.20 and 706 715 𝑅=14(𝑏+𝑐)2sec2𝐴2+(π‘βˆ’π‘)2cosec2𝐴2702 716 Distance between the centres of inscribed and circumscribed circles. =𝑅2βˆ’2π‘…π‘Ÿ936 716 Radius of circle touching 𝑏, 𝑐 and the inscribed circle π‘Ÿβ€²=π‘Ÿtan214(𝐡+𝐢)By sin𝐴2=π‘Ÿβˆ’π‘Ÿβ€²π‘Ÿ+π‘Ÿβ€²

Sources and References

https://archive.org/details/synopsis-of-elementary-results-in-pure-and-applied-mathematics-pdfdrive

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References

  1. B. Joseph, 1978, University Mathematics: A Textbook for Students of Science & Engineering
  2. Ayres, F. JR, Moyer, R.E., 1999, Schaum's Outlines: Trigonometry
  3. Hopkings, W., 1833, Elements of Trigonometry
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