Question

the length of chord of circle is 8cm if it is perpendicular distance from the centre is 3 cm the radius of circle is=​

Answer 1

To find : AO

Consider triangle AOP
AP = 4 cm ( 8/2 ) , since a perpendicular from centre to chord bisects it
OP = 3 cm , given

By pythagoras theorem ,
AP squared = OP squared + AP squared.
9+ 16 = 25 = AP squared
AP = 5 cm

Answer 2

The radius of the circle is 5 cm

Explanation:

Given that the length of the chord of circle is 8 cm if it is perpendicular distance from the center is 3 cm

We need to find the radius of the circle.

The image of the figure is attached below.

The figure contains the following measurements.

Let AM be the length of the chord. $\ {AM}=8 \ {cm}$

Let the distance of the chord from the center is $\ {OB}=3 \ {cm}$

Also, $\ {OB} \perp \ {AM}$

The length of AB and MB can be determined using

$\frac{A M}{2}=\frac{8}{2}=4 \ {cm}$

Thus, we have, $A B=M B= 4 \ cm$

Let us consider ΔOAB

Using Pythagoras theorem, we have,

$A B^{2}+O B^{2}=O A^{2}$

       $4^{2}+3^{2}=O A^{2}$

               $25=O A^{2}$

                 $5=OA$

Thus, the radius of the circle is 5 cm

Learn more:

(1) A chord of length 8cm is at a distance 3cm from the centre of the circle.calculate the radius of the circle..

please solve

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(2) The radius of a circle is 6cm . the perpendicular distance from the centre to the chord which is 8 cm in length is

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