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Question

Draw a pair of tangents to a circle of any convenient radius, which are inclined to the line joining the centre of the circle and intersect at a point forming an angle of 45 degree with the line.

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Solution

Draw a line segment AB.
Take any point O on AB.
Draw a right angle at O and mark a length of 4.5 cm on that right angle as Q. OQ is the radius of the circle.
Extend OQ. Mark a semicircle of any radius with Q as its center such that it cuts the extended OQ in P and R.
With center as P and radius equal to radius of semicircle drawn, cut an arc on semicircle.
Similarly, do it from the new arc drawn.
Repeat the procedure from the 2 new arcs. Draw a line for 90.
Similarly do it for the angle between the right angle just obtained and extended OQ.
This angle will give 135.
Mark 4.5 cm on this angle. This gives QT.
Now, draw a perpendicular for QT and let it meet AB in Z.
Draw a circle with Q as center and OQ as radius.


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