Question

Draw a circle of radius 3cm. From a point p, 6cm away from its centre, construct a pair of tangents to the circle. Measure the lengths of the tangents.

Answer 1

Step-by-step explanation:

u can do it... just see it

Answer 2

Answer:

$3\sqrt{3}$ is the length of the required tangent .

Step-by-step explanation:

Explanation:

Given , radius of circle = 3cm  and

P is the point from 6cm away from the circle

Step1:

Draw a circle of radius 3 cm from centre O

Make a point P  which is 6cm away from the circle .

Now draw perpendicular bisector of OP

Take more than half of length OP and from centre O draw arc .

Take P as centre and draw another arc which cut the previous arc.

Take M as centre and radius MP ,draw a circle and obtain point Q and R.

Now join PQ and PR ,which are our tangent .

In right angle triangle Δ OQP

⇒ $OP^{2} =OQ^{2} +PQ^{2}$

⇒$6^{2} =3^{2} +QP^{2}$

⇒36 = 9 + $QP^{2}$

⇒ QP = $\sqrt{36-9} = \sqrt{27} = 3\sqrt{3}$ cm .

So ,QP = RP = $3\sqrt{3}$ cm

Final answer :

Hence , the length of the tangent QP and RP is $3\sqrt{3}$ cm .