Respuesta :

The distance between the centre of marble to the corner of the track is [tex]\sqrt{2}[/tex] times of r

Step-by-step explanation:

At first, it is given that the radius of marble is 'r'.

Consider the centre of marble as O

Then the line from the centre of marble to the point touching the L shaped track is also 'r'. i.e., OA=r

                              (Since, the radii for a particular circle is equal throughout)

Now let's discuss the length of AC;

If we join AOBC, we get a square each of side 'r'

Then, OC can be calculated by using Pythagoras theorem,

AC=[tex]\sqrt{AC^{2} + AO^{2}}[/tex]

and AC=AO=r

Thus, AC=[tex]\sqrt{r^{2}+ r^{2} }[/tex]

AC=[tex]\sqrt{2}[/tex]r

Ver imagen rahulnair123437

The distance between the centre of marble to the corner of the track is  times of [tex]\sqrt{2}[/tex] r.

Calculation of the distance:

Since

the radius of marble is 'r'.

In the case when

we join AOBC, we get a square each of side 'r'

So, OC can be calculated by using the Pythagoras theorem,

AC=[tex]\sqrt{AC^2 + AC^2}[/tex]

and AC=AO=r

Thus, AC=[tex]\sqrt{r^2 + r^2}[/tex]

Hence, The distance between the centre of marble to the corner of the track is  times of [tex]\sqrt{2}[/tex] r.

Learn more about radius here: https://brainly.com/question/21502832

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