# The Problem

Suppose that \(PQ\) and \(RS\) are two chords of a circle intersecting at a point \(O\). It is given that \(PO=3 \text{cm}\) and \(SO=4 \text{cm}\). Moreover, the area of the triangle \(POR\) is \(7 \text{cm}^2\). Find the area of the triangle \(QOS\).

# Key Ideas

- Power of a point
- Ratio of areas of similar triangles is equal to ratio of squares on their corresponding sides

# Discussion