Secant and Tangent

Q.

A tangent is a secant with which of the following properties?

1. The secant passes through the centre of the circle.

2. The points of intersection are infinite distance apart.

3. The secant is a curved line.

4. The points of intersection are coinciding points.

Q.

The number of tangents to a circle which are parallel to a secant is two.

1. 1

2. 2

Q.

At most two tangents can be drawn parallel to a given secant because there are only two points on a circle through which the lines parallel to the secant are tangents to the circle

1. True

2. False

Q.

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:

1. Chord

2. Diameter

3. Tangent

4. Secant

Q. Fill in the blanks.
(i) A line intersecting a circle at two distinct points is called a ....... .
(ii) A circle can have ....... parallel tangents at the most.
(iii) The common point of a tangent to a circle and the circle is called the ....... .
(iv) A circle can have ...... tangents.

Q. In the given figure, PQ is a chord of length 8 cm of a circle with centre O and radius 5 cm. If the tangents to the circle at the points P and Q intersect at T, then find the length of PT.

[4 marks]

Q. Which of the following statements is not true?
(a) If a point P lies inside a circle, no tangent can be drawn to the circle passing through P.
(b) If a point P lies on a circle, then one and only one tangent can be drawn to the circle at P.
(c) If a point P lies outside a circle, then only two tangents can be drawn to the circle from P.
(d) A circle can have more than two parallel tangents parallel to a given line.

Q.

P lies in the exterior of 🔘 (O, 5 )such that op=13. Two tangents are drawn .to the circle which touch the circle in A and N.find AB

Q.

You are given a circle with radius 'r' and centre 'O'. You are asked to draw a pair of tangents which are inclined at an angle of 60° with each other, from a point E.
Refer to the figure and select the option which would lead you to the required construction. The distance d is the distance OE.

1. Using trigonometry, arrive at d = r and mark E.

2. Construct the $△$MNO as it is equilateral triangle.

3. Mark M and N on the circle such that $\angle$MOE = ${60}^{\circ }$ and $\angle$NOE = ${60}^{\circ }$.

4. Mark M and N on the circle such that $\angle$MOE = ${120}^{\circ }$ and $\angle$NOE = ${120}^{\circ }$.

Q.

Secant intersects the circle at ___ distinct points.

Q. 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:

1. Tangent
2. Secant
3. Chord
4. Diameter

Q. Secant intersects the circle at distinct points.

1. 2
2. 3
3. 4

Q.

Secant intersects the circle at ___ distinct points.

Q.

If a secant is drawn to a circle, then under any circumstance, tangents cannot be drawn parallel to the secant.

1. True

2. False

Q.

At most two tangents can be drawn parallel to a given secant because there are only two points on a circle through which the lines parallel to the secant are tangents to the circle.

1. True
2. False

Q.

At most two tangents can be drawn parallel to a given secant because there are only two points on a circle through which the lines parallel to the secant are tangents to the circle

1. True

2. False

Q.

A line which intersects a circle at two distinct points is called a ____.

1. sector

2. tangent

3. secant

4. chord

Q.

In the figure given, a circle is shown with a secant. How many tangents can be drawn parallel to the secant?

1. 1

2. 0

3. 2

4. Infinite

Q.

The tangent to a circle is a line which touches the circle at exactly ________.

1. 3 points

2. 1 point

3. 2 points

4. 4 points

Q.

If a secant is drawn to a circle, then under any circumstance, tangents cannot be drawn parallel to the secant.

1. True

2. False

Q.

___ is a line that intersects a circle at only one point, and ___ is a line that intersects the circle at two distinct points.

1. Tangent, secant

2. Secant, secant

3. Secant, tangent

4. Tangent, tangent