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# 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