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Triangle Arcs


In the above figure, the curves are arcs of a Circle and

$\displaystyle a$ $\textstyle =$ $\displaystyle BC$ (1)
$\displaystyle b$ $\textstyle =$ $\displaystyle CA=CP$ (2)
$\displaystyle c$ $\textstyle =$ $\displaystyle BA=BQ.$ (3)

PQ^2=2BP\cdot QC.
\end{displaymath} (4)

The figure also yields the algebraic identity
\end{displaymath} (5)

See also Arc


Berndt, B. C. Ramanujan's Notebooks, Part IV. New York: Springer-Verlag, pp. 8-9, 1994.

Dharmarajan, T. and Srinivasan, P. K. An Introduction to Creativity of Ramanujan, Part III. Madras: Assoc. Math. Teachers, pp. 11-13, 1987.

© 1996-9 Eric W. Weisstein