No. of Tangents to a Circle from a Given Point

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 $\angle$ B = ${90}^{\circ }$. 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 $5cm.$ 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.

1. True

2. 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 = 50⁰ and $\angle$SRM = 60⁰. 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

1. 100^o

2. 130^o

3. 120^o

4. 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

1. Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of Assertion (A).
2. Assertion (A) is true, but Reason (R) is false.
3. Assertion (A) is false, but Reason (R) is true.
4. 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 ${60}^{\circ }.$

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

1. True
2. False

Q.

In the given figure, PQ = QR, ∠RQP = 68⁰, PC & CQ are tangents to the circle with center O. Find ∠QOP, ∠PCQ.

1. 112^o, 124^o

2. 112^o, 68^o

3. 112^o, 34^o

4. 56^o, 68^o

5. 56^o, 34^o

6. 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 cm² 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?

1. P is inside the circle.

2. P is on the circle.

3. P is outside the circle.

4. 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?

1. P is on the circle.
2. O and P are coincident points.
3. P is outside the circle.
4. P is inside the circle.

Q.

A point lies inside the circle. So __ tangents can be drawn from the point to the circle. (Fill in the blanks with 0, 1, 2 or 3)

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?

1. P is outside the circle.

2. P is inside the circle.

3. P is on the circle.

4. O and P are co-incident points.