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SMO 2010 Senior Round 1 Question 22

SMO · SMO 2010 Senior Round 1

Question 22

The figure below shows a circle with diameter $AB$. $C$ and $D$ are points on the circle on the same side of $AB$ such that $BD$ bisects $\angle CBA$. The chords $AC$ and $BD$ intersect at $E$. It is given that $AE=169$ cm and $EC=119$ cm. If $ED=x$ cm, find the value of $x$.

Question illustration