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Alekssandra [29.7K]
2 years ago
7

Please help asap!the problem is in the picture

Mathematics
1 answer:
ladessa [460]2 years ago
8 0

Given:

AB=6\ BC=r,\ CD=r,\ AD=12.

To find:

The value of r.

Solution:

We have,

AB=6\ BC=r,\ CD=r,\ AD=12.

We know that the radius is perpendicular to the tangent at the point of tangency

AD is the tangent and CD is the radius. So, CD is perpendicular to AD at point D, i.e., m\angle D=90^\circ.

Using Pythagoras theorem, we get

AC^2=AD^2+CD^2

(6+r)^2=12^2+r^2

36+12r+r^2=144+r^2

12r=144+r^2-36-r^2

On further simplification, we get

12r=108

r=\dfrac{108}{12}

r=9

Therefore, the value of r is 9.

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