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Answer :

Step of construction:

1. Draw a circle with centre O and radius 3 cm

2. Produce the diameter of the circle to both the ends up to P and Q such that OP = OQ = 7cm

3. Draw the perpendicular bisector of the line PO and QO
and mark the midpoint as M and M' respectively

4. Draw arc with centre M on circle on R and S

5. Draw arc with centre M' on circle on T and U

6. PR , PS , QT and QU are the required tangents.

- Draw a circle of radius 6 cm. From a point 10 cm away from its centre, construct the pair of tangents to the circle and measure their lengths.
- 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.
- Draw a circle of radius 3 cm. Take two points P and Q on one of its extended diameter each at a distance of 7 cm from its centre. Draw tangents to the circle from these two points P and Q.
- Draw a pair of tangents to a circle of radius 5 cm which are inclined to each other at an angle of 60°
- Draw a line segment AB of length 8 cm. Taking A as centre, draw a circle of radius 4 cm and taking B as centre, draw another circle of radius 3 cm. Construct tangents to each circle from the centre of the other circle.
- Let ABC be a right triangle in which AB = 6 cm, BC = 8 cm and \(\angle B=90° \) ;. BD is the perpendicular from B on AC. The circle through B, C, D is drawn. Construct the tangents from A to this circle.
- 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.
- Q.1 Draw a circle of radius 6 cm. From a point 10 cm away from its centre, construct the pair of tangents to the circle and measure their lengths.
- Q.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.4 Draw a pair of tangents to a circle of radius 5 cm which are inclined to each other at an angle of 60°
- Q.5 Draw a line segment AB of length 8 cm. Taking A as centre, draw a circle of radius 4 cm and taking B as centre, draw another circle of radius 3 cm. Construct tangents to each circle from the centre of the other circle.
- Q. 6 Let ABC be a right triangle in which AB = 6 cm, BC = 8 cm and \(\angle \) B = 90°. BD is the perpendicular from B on AC. The circle through B, C, D is drawn. Construct the tangents from A to this circle.
- Q.7 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.

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