Finding the Center of the Circle

Q.

Draw a pair of tangents of radius 3cm that are inclined to each other at an angle of 50 degrees

Q.

A pair of tangents can be constructed from a point P to a circle of radius 3.5 cm situated at a distance of 3 cm from the centre.

1. True

2. False

Q.

Draw a circle of radius $4cm$.

Draw any two of its chords.

Construct the perpendicular bisectors of these chords.

Where do they meet?

Q.

To draw a pair of tangents to a circle which are inclined to each other at an angle of 45^oit is required to draw tangents at the end point of those two radii of the circle, the angle between which is :

1. 135^o

2. 105^o

3. 145^o

4. 70^o

Q.

An arc ACB subtends $\angle AOB$ at the centre of the circle. If 2 arcs are drawn with A and B as centre with a fixed radius such that they intersect at point P, then line OP will ___________ $\angle AOB$.

1. be at right angles to

2. bisect

3. trisect

4. be at zero angle to

Q. Question 5
In figure AB and CD are common tangents to two circles of unequal radii prove that AB=CD

Q.

In the above scenario, after drawing the circle with radius R, what is the next thing to be constructed?

1. Circle with radius ‘r’

2. The point O

3. Tangent PO

4. The point B

Q. Draw a circle of radius 3 cm . Draw a tangent which making an angle of 30 with the line passing through centre

Q.

Construct tangents to a circle of radius 4 cm from a point on the concentric circle of radius 6 cm and find its approximate length.

1. 3 cm

2. 4.5 cm

3. 3.5 cm

4. 4 cm

Q.

Question 3
State whether the following is true or false.
A pair of tangents can be constructed from a point P to a circle of radius 3.5 cm situated at a distance of 3 cm from the centre.
[Thinking process
Let r = radius of circle and d = distance of a point from the centre.
1. If r = d, then point lie on the circle i.e only one tangent is possible
2. If r < d, then point lie outside the circle. i.e a pair of tangent is possible.
3. If r>d, then point lie inside the circle i.e no tangent is possible.
]

Q.

A pair of tangents can be constructed from a point P at a distance of 3 cm from the centre of a circle whose radius is 3.5 cm.

1. True

2. False

Q. Any perpendicular drawn to a chord passes through the centre of the circle.

1. False
2. True

Q. Question 2
Construct a tangent to a circle of radius 4 cm from a point on the concentric circle of radius 6 cm and measure its length. Also verify the measurement by actual calculation.

Q. To determine the centre of a circle, we need to draw the perpendicular bisector of two chords.

1. False
2. True

Q. The perpendicular drawn from the centre of a circle bisects the chord.

1. False
2. True