Question

The length of the tangent to a circle from a point P, which is 25 cm away from the centre, is 24 cm. What is the radius of the circle.

Answer 1

Let AP be a tangent drawn from P  to a circle with Centre O such that AP = 24 cm & OB = 25 cm
We know that the tangent at any point of a circle is perpendicular to the radius through the point of contact.

In right angled ∆OAP, OA ⟂ AP,
OP² = OA² + AP²

[By Pythagoras theorem]
25² = OA² + 24²
625 = OA² + 576
OA² = 625 - 576
OA² = 49
OA = √49
OA = 7 cm

Hence, the radius of the Circle is 7 cm.

HOPE THIS WILL HELP YOU...

Answer 2

Here is your answer
----------------------------------------------------------------------------------------------------------------


The shortest distance from point P to the circle is the length of x.


hypotenuse OP equals to 

$= > \sqrt{2.5 {}^{2} } + 6 {}^{2} = 6.5$


Therefore ,

=>
X = 6.5 - 2.5 = 4