Is this a theorem?

Geometry Level 3

A line intersects the sides A B , B C , C A AB,BC,CA of a triangle A B C ABC at P , Q P,Q and R R , respectively.

What is the value of A P B P ⋅ B Q C Q ⋅ C R R A \dfrac{AP}{BP} \cdot \dfrac{BQ}{CQ} \cdot \dfrac{CR}{RA} ?


The answer is 1.

Archit Tripathi by Archit Tripathi , 23, India

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1 solution

Maria Kozlowska
Sep 11, 2016

This is similar to Ceva's Theorem with additional condition that segments A P , B Q , C R AP, BQ, CR intersect at a single point.

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