Question
Given an arc of a circle, complete the circle.
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Answer
Let arc $PQ$ of a circle be given. We have to complete the circle, which means that we have to find its centre and radius. Take a point $R$ on the arc. Join $PR$ and $RQ$. Use the construction that has been used in proving There is one and only one circle passing through three given non-collinear points., to find the centre and radius.
Taking the centre and the radius so obtained, we can complete the circle (See Figure).
Taking the centre and the radius so obtained, we can complete the circle (See Figure).
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