Question

A point P is 20cm away from the centre O of a circle and the length PT of the tangent drawn from P to the circle is 10cm. Find the radius of the circle.

Answer 1

Answer:

radius of the given circle is 17.32 cm

Step-by-step explanation:

Given, O is the centre of the circle, OP = 20 cm

also, PT is a tangent of length 10 cm

to find: radius of the circle

Let 'r' be the radius of the circle

from the figure, OT⊥ OP

apply Pythagoras theorem: OP² = OT²+ PT²

⇒ 20² = r² + 10²

$r^{2} = 400-100\\r^{2} = 300$

⇒ r² = 300

r = √300

$r = 17.32$

Hence, radius of the circle is 17.32 cm.  

Answer 2

Concept introduction:

A tangent is a type of plane or straight line which touches a curved surface via angle which is about $90$ degree.

Given:

$O$ is the centre of the circle, $OP=20cm$

also, $PT=10cm.$

To find:

We have to find the radius of the circle.

Solution:

According to the question,

Let '$r$' be the radius of the circle.

$OT$⊥$TP$

$OT^{2}=OP^{2} -PT^{2} \\= > r^{2}=20^{2} -10^{2} \\= > r=17.32$

Hence, the radius of the circle is $17.32cm$