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Diagram

Take point P and Q and draw a circle passing through them. Draw a tangent AB to the circle without using the centre of the circle.

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#### Solution

**Analysis:**

Centre of the circle passing through P and Q must be equidistant from points P and Q.

∴ It must lie of perpendicular bisector of seg PQ.**Steps of construction:**

- Take any two point P, Q and join them.
- Draw a perpendicular bisector of PQ.
- Take any point O on the perpendicular bisector and draw a circle with centre O and radius OP.
- Take any point A on the major arc of the circle and draw ∆PQA.
- By taking P as centre and any convenient distance on compass draw an arc intersecting the arms of ∠QPA in points T and R.
- With A as centre and the same distance in the compass, draw an arc intersecting the chord QA at point S.
- Taking radius equal to TR and S as centre, draw an arc intersecting the previously drawn arc. Name the point of intersection as B.
- Draw line AB. Line AB is the required tangent to the circle.

Concept: Construction of a Tangent to the Circle at a Point on the Circle

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