Question

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

Answer 1

Analysis:

As shown in the figure,

C is the center of the required circle.

∴ ∠QAC = 90°   ...[Tangent theorem]

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

∴ The center of the circle, i.e., point C, is the point of intersection of ray AC and perpendicular bisector of seg AB.

Steps of construction:

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