CIRCLE
constructing tangent and secant
Q. Draw a circle and two lines
parallel to a given line such
that one is a tangent and the
other, a secant to the circle.
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Rough Figure
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Draw a circle of suitable radius
Let us draw perpendicular from O to line l
O as centre and radius more than distance between point O and line l, draw two arcs intersecting line l at X and Y
X as centre, and radius more than half of XY, draw an arc
`
Now, with the same radius Y as centre, cut previously drawn arc
Draw line OZ
A as centre draw 2 arcs on AO
Draw perpendicular bisector of seg BC
B as centre and radius more than half of BC, draw an arc
Now C as centre and with the same radius, cut previously drawn arc
Draw ray AD
E as centre draw 2 arcs on EO
Draw perpendicular bisector of seg FG
F as centre and radius more than half of FG, draw an arc
Now G as centre and with the same radius, cut previously drawn arcs
Draw ray EH
l
Draw line l outside the circle
Consider point E