$CATEGORY: Maths - TicTacLearn/10. Circles/10. Circles--Tangent to a Circle

//Multiple Choice

The radius of a circle is perpendicular to the tangent at the point of contact. What is the angle between the radius and the tangent? {
~30°
~45°
~60°
=90°
}

A tangent to a circle touches the circle at\: {
=Exactly one point
~Exactly two points
~Any number of points
~No point
}

If the length of the tangent from a point P to a circle is 12 cm, what is the distance from P to the center of the circle, given the radius is 5 cm? {
=13 cm
~10 cm
~17 cm
~15 cm
}

The length of tangents drawn from an external point to a circle are\: {
=Always equal
~Sometimes equal
~Never equal
~Equal only for concentric circles
}

How many tangents can be drawn to a circle from an external point? {
~1
=2
~3
~Infinite
}

The distance between the center of a circle and a point on the circle is equal to the\: {
~Diameter
=Radius
~Circumference
~None of these
}

If the radius of a circle is r, then the maximum length of a chord is\: {
~r
=2r
~r2
~r/2
}

A circle can have\: {
~One tangent
~Two tangents
=Infinite tangents
~None of these
}

If two tangents are drawn to a circle from an external point, the angle between them is 60∘. What is the distance between the center of the circle and the external point if the radius is 5 cm? {
~5 cm
=10 cm
~15 cm
~20 cm
}

//True or False

A tangent to a circle can intersect the circle at more than one point. {F}

The radius of a circle is parallel to the tangent at the point of contact. {F}

The length of tangents drawn from an external point to a circle is always equal. {T}

A tangent is perpendicular to the radius at the point of contact. {T}

A circle can have only one tangent. {F}

The distance between the center and the tangent is equal to the radius. {T}

The tangents from an external point are not equal in length. {F}

If two tangents are drawn from a point outside the circle, they meet the circle at different points. {T}

The length of the tangent depends on the diameter of the circle. {F}

A tangent always lies outside the circle except at the point of contact. {T}

//Numericals



//Fill in the blanks

A tangent to a circle is always ______ to the radius at the point of contact. {
~Parallel
=Perpendicular
~Equal
~Tangent
}

The number of tangents that can be drawn to a circle from a point inside the circle is ______. {
~1
~2
~Infinite
=None
}

The distance from the center of the circle to the tangent line is equal to the ______ of the circle. {
~Diameter
=Radius
~Circumference
~Chord
}

The tangents drawn from an external point to a circle are always ______ in length. {
=Equal
~Unequal
~Twice the radius
~None of these
}

If a tangent is drawn at a point on a circle, it touches the circle at ______ point(s). {
=One
~Two
~Three
~Infinite
}

The angle between two tangents drawn from an external point to a circle subtends ______ at the center of the circle. {
~90°
~60°
~120°
=180°
}

The point where a tangent touches the circle is called the ______. {
~Center
~Chord
=Point of contact
~Diameter
}

The length of the tangent drawn from an external point to a circle is the ______ side of the right triangle formed with the radius and the line joining the center and the external point. {
~Adjacent
=Opposite
~Hypotenuse
~None
}

If the radius of a circle is 7 cm and the length of the tangent drawn from an external point is 24 cm, the distance from the external point to the center of the circle is ______ cm. {
=25
~26
~24
~30
}

A tangent to a circle intersects the circle at ______ point(s). {
=One
~Two
~Infinite
~None
}

//Match the following

Match the following items from Column A with their correct corresponding options from Column B\:
{
    =Tangent at the point of contact -> Perpendicular to radius
    =Length of tangents from an external point -> Equal
    =Number of tangents to a circle -> Infinite
    =Point where tangent touches circle -> Point of contact 
}



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