If a pair of tangents is drawn from a point outside the circle, then the distance between the two points of contact is always less than the longest chord of the circle. State whether the given statement is true or false.

True

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False

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Solution

The correct option is A
True

The distance between the two points of contact is always less than the longest chord of the circle. The longest chord is the diameter, and if the distance between the points of contact is equal to the diameter, then the tangents will be parallel which is not possible.

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If a pair of tangents is drawn from a point outside the circle, then the distance between the two point of contact of tangents is always less than the longest chord of the circle. State whether the given statement is true or false.

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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.
]

Q. Tangents are drawn to a circle from a point which always lies on a given line; prove that the locus of the middle point of the chord of contact is another circle.

Describe:

(i) The locus of points at distances less than 3 cm from a given point.

(ii) The locus of points at distances greater than 4 cm from a given point.

(iii) The locus of points at distances less than 2.5 cm from a given point.

(iv) The locus of points at distances greater than or equal to 35 mm cm from a given point.

(v) The locus of the centre of a given circle which rolls around the outside of a second circle and is always touching it.

(vi) The locus of the centres of all circles that are tangent to both the arms of a given angle.

(vii) The locus of the mid-points of all chords parallel to a given chord of a circle.

(viii) The locus of points within a circle that are equidistant from the end points of a given chord.

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If a pair of tangents is drawn from a point outside the circle, then the distance between the two points of contact is always less than the longest chord of the circle. State whether the given statement is true or false.​

The correct option is A True The distance between the two points of contact is always less than the longest chord of the circle. The longest chord is the diameter, and if the distance between the points of contact is equal to the diameter, then the tangents will be parallel which is not possible.

If a pair of tangents is drawn from a point outside the circle, then the distance between the two points of contact is always less than the longest chord of the circle. State whether the given statement is true or false.

The correct option is A
True

The distance between the two points of contact is always less than the longest chord of the circle. The longest chord is the diameter, and if the distance between the points of contact is equal to the diameter, then the tangents will be parallel which is not possible.