Question
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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Answer
Steps of Construction:
i. Draw a circle with any radius and center $O$. Here $x y$ is given line.
ii. Choose any point $P$ on the circumference of the circle, and draw a line passing through $P$, Let's name it $A B$.
iii. Draw a line $A B$ parallel to $x y$, such that $A B$ intersects the circle at two points $P$ and $A$.Here, $A B$ and $x y$ are two parallel lines. $A B$ intersects the circle at exactly two points, $P$ and $Q$. Therefore, line $A B$ is the secant of this circle.
iv. $C D$ intersects the circle at exactly one point, $R$, line $C D$ is the tangent to the circle.
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