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Diagram

AB = 6 cm, ∠BAQ = 50°. Draw a circle passing through A and B so that AQ is the tangent to the circle

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#### Solution

**Analysis:** As shown in the figure,

C is the centre of the required circle.

∴ ∠QAC = 90° ......[Tangent theorem]

∴ Centre of the circle must be on ray AC and it must be equidistant from point A and point B.

∴ The centre of the circle, i.e., point C, is the point of intersection of ray AC and perpendicular bisector of seg AB.**Steps of construction:**

- Draw seg AB of 6 cm.
- Draw ray AQ such that ∠BAQ = 50°
- Draw ray AD such that ∠QAD = 90°
- Draw perpendicular bisector of seg AB, intersecting ray AD at point C.
- With centre C, draw a circle with radius AC.

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

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