Tangent as Special Case of Secant
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A line that intersects a circle in exactly one point is called a
Tangent
Radius
Chord
Diameter
If two tangents inclined at an angle of are drawn to a circle of radius , the length of each tangent is equal to:
In a triangle ABC, ∠A=60∘ and the incircle (centre O) touches BC, CA and AB at points P, Q and R respectively.
∠QOR=120∘
∠QPR=60∘
∠QOR=90∘
∠QPR=50∘
- False
- True
The radius of a circle is 8 cm. Calculate the length of a tangent drawn to this circle from a point at a distance of 10 cm from its centre.
9 cm
7 cm
2 cm
6 cm
(i) The common point of a tangent and the circle is called ..........
(ii) A circle may have .............. parallel tangents.
(iii) A tangent to a circle intersects in it ............ point(s).
(iv) A line intersecting a circle in two points is called a ...........
(v) The angle between tangent at a point on a circle and the radius through the point is ........
A secant which meets the circle at A and B is dragged up until A, B concide at a point. What is that point called?
Point of secant
Point of contact
End Point of secant
Tangent
Two circles with centres $ \mathrm{O}$ and $ {\mathrm{O}}^{\text{}}$ of radii $ 3 \mathrm{cm}$ and $ 4 \mathrm{cm}$, respectively intersect at two points $ \mathrm{P}$ and $ \mathrm{Q}$ such that $ \mathrm{OP}$ and $ {\mathrm{O}}^{\text{}}\mathrm{P}$ are tangents to the two circles. Find the length of the common chord $ \mathrm{PQ}$.
A line segment AB intersects a circle at two distinct points C and D as it passes through its centre, as shown in the figure. The line, whose segment is AB, is a:
Tangent
Secant
Diameter
Chord
If two chords AB and CD intersect externally at P, then PC x PD = _____.
PA
PA + PB
PA - PB
PA x PB
Two circles of radii 5 cm and 3 cm are concentric. Calculate the length of a chord of the outer circle which touches the inner circle.
2 cm
8 cm
23 cm
12 cm
- Chord
- Diameter
- Secant
- Tangent
A line segment AB intersects a circle at two distinct points C and D as it passes through its centre, as shown in the figure. The line, whose segment is AB, is a:
Secant
Chord
Diameter
Tangent
A line segment AB intersects a circle at two distinct points C and D as it passes through its centre, as shown in the figure. The line, whose segment is AB, is a:
Tangent
Diameter
Chord
Secant
A line that touches a circle at only one point is called
(Assume π=227)
- 44 cm
- 22 cm
- 21 cm
- 42 cm
A tangent is a secant with which of the following properties?
The points of intersection are coinciding points.
The secant passes through the centre of the circle.
The points of intersection are infinite distance apart.
The secant is a curved line.
- The points of intersection are coinciding points.
- The secant is a curved line.
- The points of intersection are infinite distance apart.
- The secant passes through the centre of the circle.
Two circles touch externally. If their radii measure 10 cm and 8 cm, then the distance between their centres is ____cm.
36
18
16
4
Two parallel tangents of a circle meet a third tangent at points P and Q. Then, PQ subtends a right angle at the centre.
True
False
In the given figure, AB is the diameter of the circle, with centre O, and AT is the tangent calculate the numerical value of x.
50∘
58∘
98∘
28∘
- inside
- on the circle
- outside
- none of these
- 30∘
- 100∘
- 60∘
- 90∘
A line segment AB intersects a circle at two distinct points C and D as it passes through its centre, as shown in the figure. The line, whose segment is AB, is a:
Chord
Secant
Diameter
Tangent
- True
- False
Two circle touch each externally at point P. Q is a point on the common tangent through P. Then, the tangents QA and QB are equal.
True
False