Construction of Tangent When Point is on the Circle

Q. The distance between two parallel tangents to a circle is equal to the ______ of the circle.

1. radius
2. diameter
3. circumference
4. area

Q.

Draw a line segment AB of length 8 cm. Taking A as centre, draw a circle of radius and $4cm$taking B as centre, draw another circle of radius $3cm$. Construct tangents to each circle from the centre of the other circle. Give the justification of the construction

Q.

Any line segment which touches a circle at exactly one point is called the __ to the circle at that point.

Q. In the following figure, PA and PB are tangents from a point P to a circle with centre O. Then the quadrilateral OAPB must be a

1. Square
2. Rhombus
3. Cyclic quadrilateral
4. Parallelogram

Q.

We can draw one tangent to the given circle through point ____

1. Both Q and R

2. Q

3. R

4. Not possible through both Q and R

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

Q.

Divide a line segment AB of length 9 cm in the ratio 4:4 at C. Now, divide the new line segment AC in the ratio 3:2 at M.

Q. Draw a circle of radius 3 cm. Draw a pair of tangents to this circle, which are inclined to each other at an angle of ${60}^o$.

Q. A tangent from a point P outside the circle meets the circle at M. Then $\angle MOP=$ , if $\angle MPO={30}^{\circ }$.

1. ${30}^{\circ }$
2. ${60}^{\circ }$
3. ${45}^{\circ }$

Q.

In the figure is a tangent to a circle. and are two points on

the circle. If BTP = ${72}^0$ and ATB = ${43}^0$ find ABT.

Q. The distance between two parallel tangents to a circle is equal to the ______ of the circle.

1. radius
2. diameter
3. circumference
4. area

Q. Draw a circle and two lines parallel to a given line such that one is tangent and other a secant to the circle.

Q.

Find the value of $\angle$ABP if $\angle$APT = ${75}^0$

1. 105°

2. 100°

3. 80°

4. 75°

Q.

A line that touches a circle at only one point is called ________.

Q. P is a point from where only one tangent can be drawn to a circle with centre O. Then P is the circle.

1. outside
2. inside
3. on

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 inside the circle.

2. P is outside the circle.

3. P is on the circle.

4. O and P are coincident points.

Q. Draw a circle with centre $P$ and radius $3.4cm$. Take point $Q$ at a distance $5.5cm$ from the centre. Construct tangents to the circle from point $Q$.

Q.

The radius is perpendicular to the tangent at the point of contact. State whether True or False.

1. True

2. False

Q.

O is the centre of the incircle of the right triangle ABC, as shown. OQBR is of what shape?

Q. Draw a circle of radius $3cm.$ Take a point at a distance of $5.5cm$ from the centre of the circle. From point $P,$ draw two tangents to the circle.

Q.

A tangent touches a circle at

1. two points

2. three points

3. only one point

4. four points

Q. Construct a pair of tangents to a circle of radius $3cm$, which are inclined to each other at an angle of ${60}^{\circ }$

Q. Draw a circle of radius 4.5 cm and a chord PQ of length 7 cm in it. Construct a tangent at P.

Q. Draw a circle of radius 3.5 cm and construct a central angle of measure 80${}^o$ and an inscribed angled subtended by the same arc. Construct tangents at the points on the circle. Extend tangents to intersect. What do you observe?

Q. A circle of radius r has a centre O. What is first step to construct a tangent from a generic point P which is at a distance r from O?

1. With P as centre and radius < r, draw a circle and then join OP.
2. With P as centre and radius = r, draw a circle and then join OP.
3. Join OP.
4. With P as centre and radius > r, draw a circle and then join OP.

Q. $\angle OAB$ is

1. ${50}^o$
2. ${75}^o$
3. ${110}^o$
4. ${25}^o$

Q.

To draw a pair of tangents to a circle which are inclined to each other at an angle of 60^o, it is required to draw tangents at the end points to those two radii of the side, the angle between which is

1. 90^o

2. 30^o

3. 120^o

4. 45^o

Q.

The radius of a circle and the tangent are perpendicular at the point of ___ .

Q.

A circle of radius r has a centre O. What is first step to construct a tangent from a generic point P which is at a distance r from O?

1. With P as centre and radius = r, draw a circle and then join OP.

2. Join OP.

3. With P as centre and radius $>$ r, draw a circle and then join OP.

4. With P as centre and radius $<$ r, draw a circle and then join OP.

Q.

The radius is ___ the tangent at the point of contact.

1. parallel to

2. not perpendicular to

3. at an acute angle with

4. perpendicular to