Relation between Angle between "Chord and Tangent" and "Central Angle"

Q.

Draw a circle with the help of a bangle. Take a point outside the circle. Construct the pair of tangents from this point to the circle. Give the justification of the construction

Q.

In the given figure, O is the centre of the circumcircle ABC. Tangents at A and C intersect at P. Given angle $AOB={140}^{\circ }$ and angle $APC={80}^{\circ }$; find the angle BAC.

1. ${60}^{\circ }$

2. ${90}^{\circ }$

3. ${50}^{\circ }$

4. ${10}^{\circ }$

Q.

In the given diagram O is the center of the circle and CD is a tangent. $\angle$CAB and $\angle$ACD are supplementary to each other $\angle$OAC = ${30}^{\circ }$. Find the value of $\angle$OCB:

1. ${30}^{\circ }$

2. ${20}^{\circ }$

3. ${60}^{\circ }$

4. ${50}^{\circ }$

Q.

In the given figure, LMN is tangent to the circle with centre O. If $\angle$ PMN = ${60}^{\circ }$, find $\angle$ MOP.

1. ${60}^{\circ }$

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

3. ${90}^{\circ }$

4. ${120}^{\circ }$

Q.

In the figure, O is the center of the circle, PQ is tangent to the circle at A. If $\angle PAB={58}^{\circ }$, find $\angle ABQ$ and $\angle AQB$. [2 MARKS]

Q.

In the figure, B and C are the centres of the 2 circles with radii 9 cm and 3 cm respectively. Also, PQ is the transverse common tangent.
Find the length of PQ, if the centres of circles are 15 cm apart.

1. 9 cm

2. 2 cm

3. 10 cm

4. 8 cm

Q. In the given figure, AC is a tangent to the circle with centre 'O'.

The measure of $\angle ACO$ is

1. ${90}^{\circ }$
2. ${60}^{\circ }$
3. ${30}^{\circ }$
4. less than ${90}^0$

Q.

What property would you use to find angle PTQ?

1. The tangents and the chord between the points of contact form an isosceles triangle.
2. Radius is perpendicular to the tangent at the point of contact.
3. There can be only two tangents to the circle from point T.
4. Lengths of tangents drawn from an external point are equal.

Q.

In the above figure, AB and CD are direct common tangents.

1. True

2. False

Q.

In the given figure, AB is a tangent to the circle with centre P. Using the information given in the figure, find $\angle BAM$.

1. ${30}^{\circ }$

2. ${20}^{\circ }$

3. ${10}^{\circ }$

4. ${40}^{\circ }$

Q. Two circles with centres O and P, and radii 8 cm and 4 cm touch each other externally. Find the length of their common tangent QR.

1. $8$ cm
2. $7$ cm
3. $8\sqrt{2}$ cm
4. $7\sqrt{3}$ cm

Q.

In the given figure, 3 secants are drawn from point P, intersects the circle at Q, M, and R respectively. What is the value of $\angle QXR$?

1. ${100}^{\circ }$

2. ${90}^{\circ }$

3. ${60}^{\circ }$

4. ${20}^{\circ }$

Q.

In the given figure, LMN is tangent to the circle with centre O. If $\angle$ PMN = ${60}^{\circ }$, find $\angle$MOP.

1. ${30}^{\circ }$

2. ${60}^{\circ }$

3. ${90}^{\circ }$

4. ${120}^{\circ }$

Q. Question 6
In figure, AT is a tangent to the circle with centre O such that OT = 4 cm and $\angle OTA={30}^{\circ }$ . Then , AT is equal to
(A) 4 cm
(B) 2 cm
(C) 2 $\sqrt{3}$ cm
(D) 4 $\sqrt{3}$ cm

Q.

Select the statements that are true.

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

2. The tangent at any point of a circle and the radius through point are not perpendicular to each other.

3. A straight line which intersects a circle at 2 points, is called the secant.

4. All of the above

Q.

PAQ is a tangent to the circle with center O at a point A as shown in figure. If $\angle OBA={35}^{\circ }$, find the value of $\angle BAQ$ and $\angle ACB$. [4 MARKS]

Q.

In the above figure, $\frac{1}{2}\left(\angle BCA\right)=\left(\frac{1}{2}\angle BAZ\right)$

1. True

2. False

Q.

In the figure P , Q and R are the points where the incircle of $△ABC$ touches the sides :

Using the information given , $\angle RQP$ = ____

1. ${60}^{\circ }$

2. ${70}^{\circ }$

3. ${50}^{\circ }$

4. ${45}^{\circ }$

Q.

In the given diagram O is the center of the circle and CD is a tangent. $\angle$CAB and $\angle$ACD are supplementary to each other $\angle$OAC = ${30}^{\circ }$. Find the value of $\angle$OCB:

1. ${30}^{\circ }$

2. ${20}^{\circ }$

3. ${60}^{\circ }$

4. ${50}^{\circ }$

Q.

In the above figure, CM is a tangent at point C. ABCD is a square. B is the centre of the circle. BM = 10 cm, CM = 8 cm. What is the value of AD?

1. 6 cm

2. 8 cm

3. 4 cm

4. 9 cm

Q.

In the above figure, PB and PQ are tangents from point P, and MN and RN are tangents from the point N to the circle with centre O.

Select the statemeents that are true:

1. $\Delta PBO\cong \Delta MON$

2. $\Delta PBO\cong \Delta PQO$

3. $\Delta NOM\cong \Delta POQ$

4. $\Delta MON\cong \Delta RON$

Q.

In the given figure, LMN is tangent to the circle with centre O. If $\angle$ PMN = ${60}^{\circ }$, find $\angle$MOP.

1. ${30}^{\circ }$

2. ${60}^{\circ }$

3. ${90}^{\circ }$

4. ${120}^{\circ }$

Q. O is the centre of the circle and BCD is the tangent to it at C.
Then, $\angle BAC+\angle ACD$= _______.

1. 180°
2. 90°
3. 60°
4. 150°

Q.

Select the statements that are true.

1. 

   AB is a secant

2. 

   CD is a chord.

3. 

   BC is a secant

4. 

   AM is a tangent

Q.

In the given figure, LMN is tangent to the circle with centre O. If $\angle$ PMN = ${60}^{\circ }$, find $\angle$ MOP.

1. ${30}^{\circ }$

2. ${60}^{\circ }$

3. ${90}^{\circ }$

4. ${120}^{\circ }$

Q. In the above figure, O is the centre of the circle, FD is a tangent at C.Then, which of the following statement is NOT true?

1. $\angle ABC={90}^{\circ }$
2. $\angle ACB={30}^{\circ }$
3. $\angle ACD={90}^{\circ }$
4. $\angle ABC={110}^{\circ }$

Q.

In the given figure, PQ is a diameter and O is the center of the circle.

If $\angle PRT=\angle QTR={90}^{\circ }$

then which of the following statement is correct?

1. $△PSR\sim △SQT$
2. $\angle PSR=\angle SPO$
3. $△OPS\sim △OQS$
4. None of the above

Q. In the given figure, $Q$ is the center of a circle and $PM$, $PN$ are tangent segments to the circle. If $\angle MPN={40}^o$, find $\angle MQN$.

Q. In the given figure, LMN is tangent to the circle with centre O. If $\angle$ PMN = ${60}^{\circ }$, find $\angle$ MOP.

Q.

In the figure, O is the center of the circle, PQ is tangent to the circle at A. If $\angle PAB={58}^{\circ }$, find $\angle ABQ$ and $\angle AQB$. [2 MARKS]