Relation between Sides of Quadrilateral Formed by Tangents on a Circle

Q.

In the given figure, PQ is a chord of length 8 cm of a circle with centre O and radius 5 cm. If the tangents to the circle at the points P and Q intersect at 'T', then the length of PT is

1. 20 cm

2. 40 cm

3. $\frac{20}{3}cm$

4. $\frac{40}{3}cm$

Q.

The length of the tangent drawn from a point $8cm$ away from the centre of a circle of radius $6cm$ is

1. √7 cm

2. 2√7 cm

Q.

How many tangents can be drawn through a point on a circle?

1. 1

2. 3

3. 2

4. 4

Q. AC is the tangent to the circle having O as the centre at point B. What would be the length of AM?

1. 3 cm
2. 2 cm
3. 2.5 cm
4. None of these

Q. How many tangents can be drawn to a circle from a point outside the circle?

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

Q.

The length of the tangent drawn from a point 8 cm away from the center of a circle of radius 6 cm is $2\sqrt{7}$ cm.

1. √7 cm

2. 2√7 cm

Q. AC is the tangent to the circle having O as the centre at point B. What would be the length of AM?

1. 3 cm
2. 2 cm
3. 2.5 cm
4. None of these

Q.

In the figure above, DE and CE are the tangents through the point E. AF and AB are the tangents through the point F to the circle with centre M.

Also, $\angle DEM={30}^{\circ }$ and $\angle AFM={10}^{\circ }$

What is the value of $\angle MFB+\angle MEC=?$

1. ${40}^{\circ }$

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

3. $5^{\circ }$

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

Q.

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

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

1. ${70}^{\circ }$

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

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

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