# An Integral Formula Related to Inner Isoptics

### Horst Martini

Technische Universität Chemnitz, Germany### Witold Mozgawa

Uniwersytet Marii Curie-Skłodowskiej, Lublin, Poland

## Abstract

An isoptic $C_{α}$ of a strictly convex $C_{2}$-curve in the plane is the locus of all points from which $C$ is seen under the same fixed angle. The two supporting lines of $C$ through such a point determine a secant of $C$, and the envelope of all these secants is the inner isoptic of $C$ and $C_{α}$. We describe an integral formula for inner isoptics in terms of quantities that naturally occur in this geometric configuration.

## Cite this article

Horst Martini, Witold Mozgawa, An Integral Formula Related to Inner Isoptics. Rend. Sem. Mat. Univ. Padova 125 (2011), pp. 39–49

DOI 10.4171/RSMUP/125-3