1 How to draw parallel tangents to a circle Write steps of construction - Maths - Constructions

Question

1 How to draw parallel tangents to a circle Write steps of
construction

Lalit Mehra · Accepted Answer

Follow the given steps to draw parallel tangents to the
circle
Step 1: Take a point on the plane of paper and draw a circle of
given radius
Step 2: Take a point P on the circle
Step 3: Join OP
Step 4: Construct âˆ OPT = 90Â°
Step 5: Extend PO, such that it intersects the circle at Q
Step 6: Construct âˆ OQR = 90Â°
<img alt="" src=
"https://s3mn%20mnimgs%20com/img/shared/discuss_editlive/2316145/2012_03_01_16_12_11/1850703%20png">
Here, PT and QR are parallel tangents to the circle
Justification :
âˆ OPT = 90Â°
âˆ OQR = 90Â°
âˆ´ âˆ OPT +
âˆ OQR = 180Â°
â‡’ QR || PT (If transversal
intersects two lines such that a pair of consecutive interior
angles is supplementary, then two lines are parallel)

After doing this	Your work should look like this
We start with a given circle with center O, and a point P outside the circle.
1. Draw a straight line between the center O of the given circle and the given point P.
2. Find the midpoint of this line by constructing the line's perpendicular bisector. The midpoint may be inside or outside the circle, depending on the circle size and the location of the given point.
3. Place the compass on the midpoint just constructed, and set it's width to the center O of the circle.
4. Without changing the width, draw an arc across the circle in the two possible places. These are the contact points J, K for the tangents.
5. Draw the two tangent lines from P through J and K.
6. Done. The two lines just drawn are tangential to the given circle and pass through P.

1. How to draw parallel tangents to a circle . Write steps of construction .