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Class 10 Math Practical Geometry-Circles 4. For an arc draw two perpendicular bisectors of the chords \overline{P Q} and \overline{Q R} of this arc construct a circle through P Q and R .


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4. For an arc draw two perpendicular bisectors of the chords \overline{P Q} and \overline{Q R} of this arc construct a circle through P Q and R .

8. Draw two circles with radii 3.5 \mathrm{~cm} and 2 \mathrm{~cm} . If their centres are 6 \mathrm{~cm} apart then draw two transverse common tangents.
8. Draw two circles with radii  3.5 \mathrm{~cm}  and  2 \mathrm{~cm} . If their centres are  6 \mathrm{~cm}  apart then draw two transverse common tangents.

8. Draw two circles with radii 3.5 \mathrm{~cm} and 2 \mathrm{~cm} . If their centres are 6 \mathrm{~cm} apart then draw two transverse common tangents.

6. If |\overline{A B}|=4 \mathrm{~cm} and |\overline{B C}|=6 \mathrm{~cm} such that \overline{A B} is perpendicular to \overline{B C} construct a circle through points A B and C . Also measure its radius.
6. If  |\overline{A B}|=4 \mathrm{~cm}  and  |\overline{B C}|=6 \mathrm{~cm}  such that  \overline{A B}  is perpendicular to  \overline{B C}  construct a circle through points  A B  and  C . Also measure its radius.

6. If |\overline{A B}|=4 \mathrm{~cm} and |\overline{B C}|=6 \mathrm{~cm} such that \overline{A B} is perpendicular to \overline{B C} construct a circle through points A B and C . Also measure its radius.

7. In and around the circle of radius 4 \mathrm{~cm} draw a square.
7. In and around the circle of radius  4 \mathrm{~cm}  draw a square.

7. In and around the circle of radius 4 \mathrm{~cm} draw a square.

5 Inscribe a circle in an equilateral triangle A B C with each side of length 5 \mathrm{~cm} .
5 Inscribe a circle in an equilateral triangle  A B C  with each side of length  5 \mathrm{~cm} .

5 Inscribe a circle in an equilateral triangle A B C with each side of length 5 \mathrm{~cm} .

9. Draw two common tangents to two touching circles of radii 2.5 \mathrm{~cm} and 3.5 \mathrm{~cm} .
9. Draw two common tangents to two touching circles of radii  2.5 \mathrm{~cm}  and  3.5 \mathrm{~cm} .

9. Draw two common tangents to two touching circles of radii 2.5 \mathrm{~cm} and 3.5 \mathrm{~cm} .

6. Draw two equal circles of each radius 2.4 \mathrm{~cm} . If the distance between their centres is 6 \mathrm{~cm} then draw their transverse tangents.
6. Draw two equal circles of each radius  2.4 \mathrm{~cm} . If the distance between their centres is  6 \mathrm{~cm}  then draw their transverse tangents.

6. Draw two equal circles of each radius 2.4 \mathrm{~cm} . If the distance between their centres is 6 \mathrm{~cm} then draw their transverse tangents.

7. Draw two circles with radii 2.5 \mathrm{~cm} and 3 \mathrm{~cm} . If their centres are 6.5 \mathrm{~cm} apart then draw two direct common tangents.
7. Draw two circles with radii  2.5 \mathrm{~cm}  and  3 \mathrm{~cm} . If their centres are  6.5 \mathrm{~cm}  apart then draw two direct common tangents.

7. Draw two circles with radii 2.5 \mathrm{~cm} and 3 \mathrm{~cm} . If their centres are 6.5 \mathrm{~cm} apart then draw two direct common tangents.

2. Inscribe a circle in a triangle A B C with sides |A B|=5 \mathrm{~cm}|B C|=3 \mathrm{~cm}|C A|=3 \mathrm{~cm} . Also measure its in-radius.
2. Inscribe a circle in a triangle  A B C  with sides |A B|=5 \mathrm{~cm}|B C|=3 \mathrm{~cm}|C A|=3 \mathrm{~cm} . Also measure its in-radius.

2. Inscribe a circle in a triangle A B C with sides |A B|=5 \mathrm{~cm}|B C|=3 \mathrm{~cm}|C A|=3 \mathrm{~cm} . Also measure its in-radius.

4. Circumscribe a circle about an equilateral triangle A B C with each side of length 4 \mathrm{~cm} .
4. Circumscribe a circle about an equilateral triangle  A B C  with each side of length  4 \mathrm{~cm} .

4. Circumscribe a circle about an equilateral triangle A B C with each side of length 4 \mathrm{~cm} .

5. Draw a circle of radius 5 \mathrm{~cm} passing through points A and B 6 \mathrm{~cm} apart. Also find distance from the centre to the line segment A B .
5. Draw a circle of radius  5 \mathrm{~cm}  passing through points  A  and  B 6 \mathrm{~cm}  apart. Also find distance from the centre to the line segment  A B .

5. Draw a circle of radius 5 \mathrm{~cm} passing through points A and B 6 \mathrm{~cm} apart. Also find distance from the centre to the line segment A B .

4. Draw two perpendicular tangents to a circle of radius 3 \mathrm{~cm} .
4. Draw two perpendicular tangents to a circle of radius  3 \mathrm{~cm} .

4. Draw two perpendicular tangents to a circle of radius 3 \mathrm{~cm} .

4. For an arc draw two perpendicular bisectors of the chords \overline{P Q} and \overline{Q R} of this arc construct a circle through P Q and R .
4. For an arc draw two perpendicular bisectors of the chords  \overline{P Q}  and  \overline{Q R}  of this arc construct a circle through  P Q  and  R .
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4. For an arc draw two perpendicular bisectors of the chords \overline{P Q} and \overline{Q R} of this arc construct a circle through P Q and R .

11. Draw circles which touches both the arms of angles (ii) 60^{\circ} .
11. Draw circles which touches both the arms of angles (ii)  60^{\circ} .

11. Draw circles which touches both the arms of angles (ii) 60^{\circ} .

1. Circumscribe a circle about a triangle A B C with sides |A B|=6 \mathrm{~cm} |B C|=3 \mathrm{~cm} |C A|=4 \mathrm{~cm} Also measure its circum radius.
1. Circumscribe a circle about a triangle  A B C  with sides |A B|=6 \mathrm{~cm}  |B C|=3 \mathrm{~cm}  |C A|=4 \mathrm{~cm} Also measure its circum radius.

1. Circumscribe a circle about a triangle A B C with sides |A B|=6 \mathrm{~cm} |B C|=3 \mathrm{~cm} |C A|=4 \mathrm{~cm} Also measure its circum radius.

3 . (ii) If |\overline{A B}|=3.5 \mathrm{~cm} and |\overline{B C}|=5 \mathrm{~cm} are the lengths of two chords of an arc then locate the centre of the arc.
 3 . (ii) If  |\overline{A B}|=3.5 \mathrm{~cm}  and  |\overline{B C}|=5 \mathrm{~cm}  are the lengths of two chords of an arc then locate the centre of the arc.

3 . (ii) If |\overline{A B}|=3.5 \mathrm{~cm} and |\overline{B C}|=5 \mathrm{~cm} are the lengths of two chords of an arc then locate the centre of the arc.

6. Circumscribe and inscribe circles with regard to a right angle triangle with sides 3 \mathrm{~cm} 4 \mathrm{~cm} and 5 \mathrm{~cm} .
6. Circumscribe and inscribe circles with regard to a right angle triangle with sides  3 \mathrm{~cm} 4 \mathrm{~cm}  and  5 \mathrm{~cm} .

6. Circumscribe and inscribe circles with regard to a right angle triangle with sides 3 \mathrm{~cm} 4 \mathrm{~cm} and 5 \mathrm{~cm} .

2. Practically find the centre of an arc A B C .
2. Practically find the centre of an arc  A B C .

2. Practically find the centre of an arc A B C .

3. Escribe a circle opposite to vertex A to a triangle A B C with sides |A B|=6 \mathrm{~cm}|B C|=4 \mathrm{~cm}|C A|=3 \mathrm{~cm} . Find its radius also.
3. Escribe a circle opposite to vertex  A  to a triangle  A B C  with sides  |A B|=6 \mathrm{~cm}|B C|=4 \mathrm{~cm}|C A|=3 \mathrm{~cm} . Find its radius also.

3. Escribe a circle opposite to vertex A to a triangle A B C with sides |A B|=6 \mathrm{~cm}|B C|=4 \mathrm{~cm}|C A|=3 \mathrm{~cm} . Find its radius also.

5. Two equal circles are at 8 \mathrm{~cm} apart. Draw two direct common tangents of this pair of circles.
5. Two equal circles are at  8 \mathrm{~cm}  apart. Draw two direct common tangents of this pair of circles.
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5. Two equal circles are at 8 \mathrm{~cm} apart. Draw two direct common tangents of this pair of circles.

9 . Circumscribe a regular hexagon about a circle of radius 3 \mathrm{~cm} .
 9 .  Circumscribe a regular hexagon about a circle of radius  3 \mathrm{~cm} .
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9 . Circumscribe a regular hexagon about a circle of radius 3 \mathrm{~cm} .

1. Divide an arc of any length(ii) into four equal parts.
1. Divide an arc of any length(ii) into four equal parts.
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1. Divide an arc of any length(ii) into four equal parts.

1. Divide an arc of any length(i) into two equal parts.
1. Divide an arc of any length(i) into two equal parts.
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1. Divide an arc of any length(i) into two equal parts.

11. Draw circles which touches both the arms of angles (i) 45^{\circ}
11. Draw circles which touches both the arms of angles (i)  45^{\circ}
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11. Draw circles which touches both the arms of angles (i) 45^{\circ}

3. (i) If |\overline{A B}|=3 \mathrm{~cm} and |\overline{B C}|=4 \mathrm{~cm} are the lengths of two chords of an arc then locate the centre of the arc.
3. (i) If  |\overline{A B}|=3 \mathrm{~cm}  and  |\overline{B C}|=4 \mathrm{~cm}  are the lengths of two chords of an arc then locate the centre of the arc.
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3. (i) If |\overline{A B}|=3 \mathrm{~cm} and |\overline{B C}|=4 \mathrm{~cm} are the lengths of two chords of an arc then locate the centre of the arc.

10. Draw two common tangents to two intersecting circle of radii 3 \mathrm{~cm} and 4 \mathrm{~cm} .
10. Draw two common tangents to two intersecting circle of radii  3 \mathrm{~cm}  and  4 \mathrm{~cm} .
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10. Draw two common tangents to two intersecting circle of radii 3 \mathrm{~cm} and 4 \mathrm{~cm} .

8 . In and around the circle of radius 3.5 \mathrm{~cm} draw a regular hexagon.
 8 .  In and around the circle of radius  3.5 \mathrm{~cm}  draw a regular hexagon.
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8 . In and around the circle of radius 3.5 \mathrm{~cm} draw a regular hexagon.

2. Construct a circle with diameter 8 \mathrm{~cm} . Indicate a point C 5 \mathrm{~cm} away from its circumference. Draw a tangent from point C to the circle without using its centre.
2. Construct a circle with diameter  8 \mathrm{~cm} . Indicate a point  C 5 \mathrm{~cm}  away from its circumference. Draw a tangent from point  C  to the circle without using its centre.
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2. Construct a circle with diameter 8 \mathrm{~cm} . Indicate a point C 5 \mathrm{~cm} away from its circumference. Draw a tangent from point C to the circle without using its centre.

3. Construct a circle of radius 2 \mathrm{~cm} . Draw two tangents making an angle of 60^{\circ} with each other.
3. Construct a circle of radius  2 \mathrm{~cm} . Draw two tangents making an angle of  60^{\circ}  with each other.
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3. Construct a circle of radius 2 \mathrm{~cm} . Draw two tangents making an angle of 60^{\circ} with each other.

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