Relation between Tangent and Intersecting Line

Q.

If two tangents inclined at an angle ${60}^{\circ }$ are drawn to a circle of radius $3cm,$ then the length of each tangent is
(A) $\frac{3}{2}$$\sqrt{3}cm$
(B) $6cm$
(C) $3cm$
(D) 3 $\sqrt{3}cm$

Q.

In the adjoining figure, O is the center of the circle and AB is the diameter. Tangent PQ touches the circle at D. $\angle$BDQ = ${48}^{\circ }$. Find the ratio of $\angle$DBA to $\angle$DCB

1. 

2. 

3. 

4. Cant be determined

Q.

The angle between the tangent at a point on a circle and the radius at the point of contact is

1. 180^o

2. 90^o

3. 45^o

4. 60^o

Q.

$O$ is the center of circle.$AB$ and $AC$ are tangent drawn from $A$ and $BA$ perpendicular to $AC$. Prove that $BACO$is a square.

Q.

Prove that the lengths of tangents drawn from an external point to a circle are equal. Using the above, prove the following:

A quadrilateral ABCD is drawn to circumscribe a circle. Prove that AB + CD = AD + BC

Q.

In the picture below, the radius of the circle is 15 cm. $\angle QOR=120°$. Select the statements that are true.

1. PR = 18√3 cm

2. PQ = 18√3 cm

3. PQ = 15√3 cm

4. PR = 15√3 cm

Q.

Tangents from a point P are drawn onto a circle with angle between them as ${120}^{\circ }$ . The tangents from P meet the circle at A and B. If a line is drawn from point P through the center of the circle O, the value of $\angle$POA is

1. 90⁰

2. 25⁰

3. 30⁰

4. 45⁰

Q.

The given figure shows a circle with centre O and BCD is tangent to it at C. Then, $\angle ACD+\angle BAC=$ __________

1. $\angle ACD={90}^0$

2. $\angle ACD={70}^0$

3. $\angle ACD={10}^0$

4. $\angle ACD={40}^0$

Q. Which of the following statements is not true?
(a) A line which intersects a circle at 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.

Q. Question 10
AB is a diameter of a circle and AC is the chord such that $\angle$ BAC = ${30}^{\circ }$. If the tangent at C intersects AB extended at D, then BC = BD.

Q.

In the given figure 'O' is the center of the circle. SP and TP are the two tangents at S and T respectively. $\angle SPT$ is ${50}^{\circ }$, the value of $\angle SQT$ is:

1. 65°

2. 125°

3. None of the above

4. 115°

Q.

In the given fig. a circle is inscribed in a quadrilateral ABCD in which $\angle$B = ${90}^0$. If AD = 23 cm AB = 29 cm and DS = 5 cm, find the radius of the circle (in cm).

Q.

In the given fig. a circle is inscribed in a quadrilateral ABCD in which $\angle$B = ${90}^0$. If AD = 23 cm AB = 29 cm and DS = 5 cm, find the radius of the circle.

Q. In the given figure, O is the centre of the circle and AB is the tangent at B. If AB = 12 cm and AD = 30 cm, calculate the diameter of the circle. [1 mark]

Q. Two tangents are drawn to a circle and the angle between them is ${30}^{\circ }$. What is the angle between the radii that are drawn at the point of contact of these two tangents.

1. ${30}^{\circ }$
2. ${60}^{\circ }$
3. ${90}^{\circ }$
4. ${150}^{\circ }$

Q.

The centre of a circle is O. There is a line XY which shares one common point with the circle. A line segment OP is drawn from O to line XY such that P is a point on line XY. What happens if P lies on the circle?

1. This situation holds no signifiance

2. OP need not be radius of circle

3. OP is perpendicular to XY

4. The angle between OP and XY is variable

Q. Question 1
If a chord AB subtends an angle of ${60}^{\circ }$ at the centre of a circle, then angle between the tangents at A and B is also ${60}^{\circ }$.

Q.
From the given figure, pair with the correct parts of the circle with their names.

1. Radius
2. Major arc
3. Major sector
4. Minor segment
5. OACB
6. ADB
7. OA
8. ACB

Q.

Find the value of x in the figure below.

1. 20 cm

2. 3 cm

3. 9 cm

4. 12 cm

Q. Match the following with its correct value of PA

1. 6cm
2. 10cm
3. 4cm

Q.

If TP and TQ are two tangents drawn to a circle with center O such that $\angle$POQ $={110}^{\circ }$, then, $\angle$PTQ is equal to:

1. 60°

2. 70°

3. 80°

4. 90°

Q.

If $△ABC$ is isosceles with AB = AC, prove that the tangent at A to the circumcircle of $△ABC$ is parallel to BC. [2 MARKS]

Q. What is the angle between the tangents if the corresponding radii are inclined at an angle of ${90}^{\circ }$?

1. ${45}^{\circ }$
2. ${90}^{\circ }$
3. ${180}^{\circ }$
4. $0^{\circ }$

Q.

In the given fig. a circle is inscribed in a quadrilateral ABCD in which $\angle$B = ${90}^0$. If AD = 23 cm AB = 29 cm and DS = 5 cm, find the radius of the circle (in cm).

___

Q.

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

1. 4 points

2. 3 points

3. 1 point

4. 2 points

Q.

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

1. 2 points

2. 3 points

3. 4 points

4. 1 point