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`Plane TrigonometryβThe Triangle and CircleβSources and References`

# Plane Trigonometry

## The Triangle and Circle

Let π = radius of inscribed circle ππ = radius of eseribed circle touching the side π π = radius of circumscribing circle 709 π=β³π From Fig., β³=ππ2+ππ2+ππ2 710 π=πsinπ΅2sinπΆ2cosπ΄2By π=πcotπ΅2+πsinπΆ2 711 ππ=β³π βπBy β³=πππ2+πππ2βπππ2 712 ππ=πcosπ΅2cosπΆ2cosπ΄2By π=ππtanπ΅2+πtanπΆ2 713 π=π2sinπ΄=πππ4β³By III.20 and 706 715 π=14(π+π)2sec2π΄2+(πβπ)2cosec2π΄2702 716 Distance between the centres of inscribed and circumscribed circles. =π2β2ππ936 716 Radius of circle touching π, π and the inscribed circle πβ²=πtan214(π΅+πΆ)By sinπ΄2=πβπβ²π+πβ²

## Sources and References

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

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ID: 210900006 Last Updated: 9/6/2021 Revision: 0 Ref:

References

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

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