The distance between a point P and the centre of a circle is 'd'. The given circles radius is r. Then what is the minimum distance between the circle and the point.

d-r

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d+r

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r-d

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2d-r

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Solution

The correct options are
A
d-r

C
r-d

The circle given is as below

Case 1

There are 2 cases possible. One is when the point is outside the circle and the other when inside it.

When its outside. Shortest distance=d-r

Case 2= When point is inside

In this case the shortest distance is the difference between 'd' and 'r' as you can see from the figure.

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A tangent is drawn to a circle of radius r from an external point P .If length of tangent from a point to the circle is twice the minimum distance between circle and the point, what is the length of the tangent?

Question 3
State whether the following is true or false.
A pair of tangents can be constructed from a point P to a circle of radius 3.5 cm situated at a distance of 3 cm from the centre.
[Thinking process
Let r = radius of circle and d = distance of a point from the centre.
1. If r = d, then point lie on the circle i.e only one tangent is possible
2. If r < d, then point lie outside the circle. i.e a pair of tangent is possible.
3. If r>d, then point lie inside the circle i.e no tangent is possible.
]

The shortest distance between a circle and an external point is r. The radius of the circle is also 'r'. What is the length of tangent from that point to the circle?

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