# Draw a circle of radius 6 cm. From a point 10 cm away from its centre,

Question:

Draw a circle of radius 6 cm. From a point 10 cm away from its centre, construct the pair of tangents to the circle and measure their lengths.

Solution:

Given that

Construct a circle of radius , and form its centre, construct the pair of tangents to the circle.

Find the length of tangents.

We follow the following steps to construct the given tep of construction

Step: I- First of all we draw a circle of radius .

Step: II- Make a point P at a distance of , and join .

Step: III -Draw a right bisector of , intersecting at Q .

Step: IV- Taking as centre and radius , draw a circle to intersect the given circle at T and T’.

Step: V- Joins PT and PT’ to obtain the require tangents.

Thus, are the required tangents.

Find the length of tangents. As we know that $O T \perp P T$ and $\triangle O P T$ is right triangle.

Therefore,

$O T=6 \mathrm{~cm}$ and $P O=10 \mathrm{~cm}$

In $\triangle O P T$,

$P T^{2}=O P^{2}-O T^{2}$

$=10^{2}-6^{2}$

$=100-36$

$=64$

$P T=\sqrt{64}$

$=8$

Thus, the length of tangents $=8 \mathrm{~cm}$