Question

the length of a tangent from a point 5 cm from the centre of the circle is 4 cm find the diameter of the circle​

Answer 1

ANSWER:-

Given:

The length of a tangent from a point 5cm from the centre of the circle is 4cm.

To find:

Find the diameter of the circle.

Solution:

Shown a figure, above attachment.

AB is a tangent drawn on that circle from point A.

Therefore,

OB⊥AB

⏺️OA=5cm

⏺️AB=4cm

In ∆ABO

Using Pythagoras Theorem:

OA² = AB² + BO²

=) 5² = 4² + BO²

=) 25 =16+ BO²

=) BO² = 25-16

=) BO= √9

=) BO= 3cm

So, radius= 3cm

Therefore,

We know that, diameter= 2r

=) 2× 3cm

=) 6cm

Hence,

The diameter of the circle is 6cm.

Hope it helps ☺️