Tangents through a Point

Q.

A line which intersects a circle at 2 distinct points is called a

1. Secant

2. Chord

3. No Term

4. Tangent

Q. Question 162
Find the values of x and y in the following kite.

Q.

The tangent at any point of a circle and the radius through this point are perpendicular to each other.

1. False

2. True

Q.

Number of tangents, that can be drawn to a circle, parallel to a given chord is

1. Zero

2. 2

3. 3

4. Infinite

Q. Question 1
If Radii of two concentric circles are 4 cm and 5 cm, then length of each chord of one circle which is tangent to the other circle, is
(A) 3 cm
(B) 6 cm
(C) 9 cm
(D) 1 cm

Q. In Fig. 7, two equal circles, with centres O and O', touch each other at X. OO' produced meets the circle with centre O' at A. AC is tangent to the circle with centre O, at the point C. O'D is perpendicular AC.

Find the value of $\frac{D{O}^{\prime }}{CO}$.

Q. Question 48
PQRS is a trapezium in which $PQ\parallel SR$ and $\angle P={130}^{\circ },\angle Q={110}^{\circ }$. Then, $\angle R$ is equal to
a) ${70}^{\circ }$
b) ${50}^{\circ }$
c) ${65}^{\circ }$
d) ${55}^{\circ }$

Q. Question 2
In Fig. 10.11, if TP and TQ are the two tangents to a circle with centre O so that $\angle POQ={110}^{\circ },then\angle PTQ$ is equal to
(A) ${60}^{\circ }$
(B) ${70}^{\circ }$
(C) ${80}^{\circ }$
(D) ${90}^{\circ }$

Q. Prove that the lengths of the tangents drawn from an external point to a circle are equal.

Q.

Which of the following is/are the types of common tangents?

1. Drawn at the point of intersection.

2. Direct common tangent

3. Transverse common tangent

4. Parallel to the chord

Q.

The chord that touches a circle at exactly one point is called _____.

1. secant
2. tangent
3. diameter
4. segment

Q.

For an incircle of a triangle, the sides of the triangle are ___ of the incircle.

1. chords

2. segment of circle

3. tangent of a circle

4. diameter of circle

Q.

TA and TB are tangents to a circle with centre O from an external point T. OT intersects the circle at point P. Then prove that AP bisects $\angle TAB$.

Q. What is the maximum number of tangents that can be drawn on a circle from a point outside the circle?

1. 1
2. 0
3. 4
4. 2

Q. The maximum number of tangents that can be drawn to a circle from a point outside it is ______
(A) 2
(B) 1
(C) one and only one
(D) 0

Q.

How many tangents can be drawn at any point on the circle?

1. 1

2. 0

3. 3

4. 2

Q. The maximum number of tangents that can be drawn at a point on the circle is:

1. 1
2. 2
3. 3
4. 4

Q. Question 3
If tangents PA and PB from a point P to a circle with centre O are inclined to each other at an angle of ${80}^{\circ },$ then $\angle POA$ is equal to
(A) ${50}^{\circ }$
(B) ${60}^{\circ }$
(C) ${70}^{\circ }$
(D) ${80}^{\circ }$

Q. Prove that the intercept of a tangent between two parallel tangents to a circle subtends a right angle at a center.

Q. AP is the tangent to the circle with centre O and radius 8 cm . If AB = 9 cm, then find the length of tangent AP.

Q.

In the given figure $△ABC$ is isosceles with AB = AC and is inscribed in a circle. If DAE is a tangent to the circle, then which of the following statement is true?

1. DE // BC
   
   

2. $△ABC$ is equilateral
   
   

3. DE intersects BC
   
   

4. None of these

Q.

In the given figure, find $a+b+c+d$.

1. ${180}^{\circ }$

2. ${360}^{\circ }$

3. ${100}^{\circ }$

4. ${210}^{\circ }$

Q.

In the given figure, there are two concentric circles with center O such that AP is tangent to the bigger circle and AB is tangent to the smaller circle. If $\angle APB=\angle ABP={30}^{\circ },OA=3$ cm and OP = 5 cm, then, radius of the smaller circle is

1. $5cm$

2. $\sqrt{5}cm$

3. $6cm$

4. $\sqrt{6}cm$

Q. In the given figure, there are two concentric circles with center O such that AP is tangent to the bigger circle and AB is tangent to the smaller circle. If $\angle APB=\angle ABP={30}^{\circ },OA=3$ cm and OP =5 cm, then, radius of the smaller circle is

1. $\sqrt{6}cm$
2. 5 cm
3. $\sqrt{5}cm$
4. 6 cm

Q. 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.

1. $$6cm$$
2. $$9cm$$
3. $$8cm$$
4. 
   $$4cm$$

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, then find the measure of $\angle$POA.

1. ${25}^{\circ }$

2. ${30}^{\circ }$

3. ${45}^{\circ }$

4. ${90}^{\circ }$

Q. The maximum number of tangents that can be drawn at a point on the circle is:

1. 1
2. 3
3. 4
4. 2

Q. $\text{From the given figure, find}\angle AOB\text{(in degrees )}.$ [2 Marks]

Q. In the given figure, O is the centre of a circle of radius 5 cm, T is a point such that OT= 13 cm and OT intersects the circle at E. If AB is the tangent to the circle at E, find the length of AB.

Q. $\text{In the given figure, a circle touches the}\text{side BC of}\Delta ABC\text{at P. AB and AC are}\text{two tangents drawn from a point A}\text{outside the circle. If AQ = 15 cm, find}\text{the perimeter of}\Delta ABC.$