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SMO 2017 Senior Round 1 Question 35

SMO · SMO 2017 Senior Round 1

Question 35

In the figure below, the circle centred at $A$ has radius 20 cm and the circle centred at $B$ has radius 5 cm. The line segment $QR$ is tangent to the smaller circle at the point $P$. Let $|QB|$ and $|BR|$ denote the length of the line segment $QB$ and $BR$ respectively. Find the value of $|QB|\times|BR|$.

Question illustration