Triangle Arcs

$\begin{figure}\begin{center}\BoxedEPSF{TriangleArcs.epsf}\end{center}\end{figure}$

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

Then

$\begin{displaymath} PQ^2=2BP\cdot QC. \end{displaymath}$

(4)

The figure also yields the algebraic identity

$\begin{displaymath} (b+c-\sqrt{b^2+c^2}\,)^2=2(\sqrt{b^2+c^2}-b)(\sqrt{b^2+c^2}-c). \end{displaymath}$

(5)

See also Arc

References

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.