# No. of Tangents to a Circle from a Given Point

## Trending Questions

**Q.**

How many tangents can a circle have?

**Q.**

Draw a circle of radius 3.5 cm. Draw the tangents to the circle which are perpendicular to each other.

**Q.**AP and PQ are tangents drawn from a point A to a circle with centre O and radius 9 cm. If OA = 15 cm, then AP + AQ =

(a) 12 cm

(b) 18 cm

(c) 24 cm

(d) 36 cm

**Q.**

The number of tangents that can be drawn from an external point to a circle is

(a) 1 (b) 2 (c) 3 (d) 4

**Q.**Let ABC be a right triangle in which AB = 3 cm, BC = 4 cm and ∠ B = 90∘. BD is the perpendicular from B on AC. The circle through B, C, D is drawn. Construct the tangents from A to this circle. [4 MARKS]

**Q.**Draw a circle of radius 3 cm and take a point P outside it. Without using the centre of the circle, draw two tangents to the circle from the point P. [4 MARKS]

**Q.**

Draw a circle of radius 5 cm. Take a point P on it. Without using the centre of the circle construct a tangent at the point P. [3 MARKS]

**Q.**

A pair of tangents can be constructed from a point P at a distance of 3 cm from the centre of a circle whose radius is 3.5 cm.

True

False

**Q.**Question 1

Draw a circle of radius 6 cm. From a point 10 cm away from its centre, construct a pair of tangents to the circle and measure their lengths.

**Q.**In Fig. 10.86, PQL and PRM are tangents to the circle with centre O at the points Q and R respectively and S is a point on the circle such that $\angle $SQL = 50

^{0 }and $\angle $SRM = 60

^{0}. Then , find $\angle $QSR.

figure

**Q.**

Construct a circle of radius 7cm. From a point 10 cm away from its centre, draw tangents to the circle. [4 MARKS]

**Q.**

PT and PS are tangents drawn to a circle, with centre C, from a point P. If ∠TPS = 50^{O}, then the measure of ∠TCS is

100

^{o}130

^{o}120

^{o}150

^{o}

**Q.**To draw a pair f tangents to a circle which are inclined to each other at an angle of 100°, It is required to draw tangents at end points of those two radii of the circle, the angle between which should be:

(a) 100°

(b) 50°

(c) 80°

(d) 200°

**Q.**Directions: In the following questions, a statement of Assertion (A) is followed by a statement of Reason (R).

Mark the correct choice as:

Assertion (A): If in a circle, the radius of the circle is 3 cm and the distance of a point from the centre of a circle is 5 cm, then length of the tangent will be 4 cm.

Reason (R): (Hypotenuse)

^{2}= (Base)

^{2}+ (Height)

^{2}

- Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of Assertion (A).
- Assertion (A) is true, but Reason (R) is false.
- Assertion (A) is false, but Reason (R) is true.
- Both Assertion (A) and Reason (R) are true, and Reason (R) is the correct explanation of Assertion (A).

**Q.**

Write the steps of construction for drawing a pair of tangents to a circle of radius 3 cm, which are inclined to each other at an angle of 60∘.

**Q.**Draw a circle of radius 2.7 cm and draw a chord PQ of length 4.5 cm.

Draw tangents at points P and Q without using centre.

**Q.**

Which of the following statements is not true ?

(a) A line which intersects a circle in two points, is called a secant of the circle.

(b) A line intersecting a circle at one point only, is called a tangent to the circle.

(c) The point at which a line touches the circle, is called the point of contact.

(d) A tangent to the circle can be drawn from a point inside the circle.

Assertion-and-Reason Type

Each quation consists of two statements, namely Asserction (A) and Reason (R). For selecting the correct answer, use the following code;

(a) Both Assertion (A) and Reasson (R) are true and Reason (R)

is a correct explanation of Assertion (A).

(b) Bothe Assertion (A) and Reason (R) are true but Reason (R) is not a correct explanation of Assertion (A).

(c) Assertion (A) is true and Reason (R) is false.

(d) Assertion (A) is false and Reason (R) is true.

**Q.**

Which of the following stateements 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 the circle, then one and only tangent can eb drawn to the circle at P.

(c) If a point P lies outside the 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.**

The length of the tangent from an external point on a circle is always greater than the radius of the circle. Write ‘True’ or ‘False’ and justify your answer.

- True
- False

**Q.**

In the given figure, PQ = QR, ∠RQP = 68^{0}, PC & CQ are tangents to the circle with center O. Find ∠QOP, ∠PCQ.

112

^{o}, 124^{o}112

^{o}, 68^{o}112

^{o}, 34^{o}56

^{o}, 68^{o}56

^{o}, 34^{o}56

^{o}, 124^{o}

**Q.**Draw a circle of a diameter 7 cm. Take a point A as the end point of diameter. Draw a tangent to the circle at the point A. [3 MARKS]

**Q.**

Construct a circle of radius 7cm. From a point 10 cm away from its centre, draw tangents to the circle.

**Q.**The length of tangent from a point A at a distance of 5 cm from the centre of the circle is 4 cm. What is the radius of the circle?

**Q.**Question 3

Draw a circle of radius 3 cm. Take two points P and Q on one of its extended diameter each at a distance of 7 cm from its centre. Draw tangents to the circle from these two points P and Q.

**Q.**In the given figure, a triangle ABC is drawn to circumscribe a circle of radius 2 cm such that the segments BD and DC into which BC is divided by the point of contact D are, of lengths 4 cm and 3 cm respectively. If the area of △ABC = 21 cm

^{2}then find the lengths of sides of AB and AC. [CBSE 2011]

**Q.**

ΔABC is an isosceles triangle in which AB = AC and sides of the triangle touch the circle at P, Q and R. Prove that Q is the mid point of the base BC.

**Q.**

There is a circle with centre O. P is a point from where only one tangent can be drawn to this circle. What can we say about P?

P is inside the circle.

P is on the circle.

P is outside the circle.

None of these

**Q.**There is a circle with center O. P is a point from where only one tangent can be drawn to this circle. What can we say about P?

- P is on the circle.
- O and P are coincident points.
- P is outside the circle.
- P is inside the circle.

**Q.**

A point lies inside the circle. So

**Q.**

There is a circle with centre O. P is a point from where only one tangent can be drawn to this circle. What can we say about P?

P is outside the circle.

P is inside the circle.

P is on the circle.

O and P are co-incident points.