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