Question

The length of a tangent drawn from a point is 4/3 times the radius then what is the distance of the point from the circle

Answer 1

Step-by-step explanation:

2

3

r

Explanation:

enter image source here

From the diagram.

A

B

=

4

3

r

The angle bisector of

B

A

C

always passes through the centre of the circle. This is the line

A

O

. Since the radius always forms an angle of

90

∘

at the point of tangency.

∠

A

B

O

and

∠

A

C

O

=

90

∘

By Pythagoras' theorem:

A

O

=

√

(

4

3

r

)

2

+

r

2

The shortest distance is the line

A

D

Since

D

O

=

r

A

D

=

A

O

−

D

O

=

√

(

4

3

r

)

2

+

r

2

−

r

A

D

=

√

r

2

(

25

9

)

−

r

=

5

3

√

r

2

−

r

For

∣

∣

√

r

2

∣

∣

=

5

3

r

−

r

=

2

3

r

Answer 2

Answer:

Please refer to the Image!

Step-by-step explanation:

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