A marble with radius r rolls in an L-shaped track. how far is the center of the marble from the corner of the track?

The distance between the centre of marble to the corner of the track is 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=

and AC=AO=r

Thus, AC=

AC=r

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