MathDB

A right that passes through the incircle

I

of the triangle

\Delta ABC

intersects the side

AB

and

CA

P

, respective

Q

. We denote BC\equal{}a\ , \ AC\equal{}b\ ,\ AB\equal{}c and \frac{PB}{PA}\equal{}p\ ,\ \frac{QC}{QA}\equal{}q. i) Prove that: a(1\plus{}p)\cdot \overrightarrow{IP}\equal{}(a\minus{}pb)\overrightarrow{IB}\minus{}pc\overrightarrow{IC} ii) Show that a\equal{}bp\plus{}cq. iii) If a^2\equal{}4bcpq, then the rights

AI\ ,\ BQ

and

CP

are concurrents.

Problem Statement