Question

Draw a circle with center P and radius \[3.4cm\] . Take point Q at a distance \[5.5cm\] from the center. Construct tangents to the circle from the point Q.

Answer 1

Hint: To construct a tangent we first need to construct the circle with the given radius and the extension with the given measurements.
Then by taking the center as the extended line’s endpoint, draw two arcs or a circle that touches the circle and mark those points.
Then by joining these points with the extended point will give us the tangents.

Complete step by step answer:
We aim to construct the tangents to the circle of a radius \[3.4cm\] from the point that was extended from the center to the outside of the circle.
First, let us construct the circle of the radius \[3.4cm\] with center P.

Now let us construct a line segment PQ of measure \[5.5cm\] from the center of the circle P.

Now we have to construct the tangents from the point Q. Now let us take a compass to draw a circle that touches the circle with a center point as Q and radius \[5.5cm\] (that is with radius PQ).
Now we can see that the big circle intersects the small circle at two points. Let us name those points A and B.

Now let us join the points QA and QB by a line segment.

Thus, the line segments AQ and BQ are the two tangents of the circle of radius \[3.4cm\] .
Hence, we have constructed the tangents of the circle.

Note: From any point outside the circle, we can construct two tangents to that circle.
We can also construct the tangent by finding the midpoint of the line PQ and with the help of compass draw arcs that cut the circle by taking the radius as a line joining the point P and that midpoint.
And joining those points to the point outside the circle will give us the tangents of the circle.