Exercise 11.1
In each of the following, give the justification of the construction also:
Question 1. Draw a line segment of length 7.6 cm and divide it in the ratio 5: 8. Measure the two parts.
Question 2. Construct a triangle of sides 4 cm, 5 cm and 6 cm and then a triangle similar to it whose sides are 2/3 of the corresponding sides of the first triangle.
Question 3. Construct a triangle with sides 5 cm, 6 cm and 7 cm and then another triangle whose sides are 7/5 of the corresponding sides of the first triangle.
Question 4. Construct an isosceles triangle whose base is 8 cm and altitude 4 cm and then another triangle whose sides are 11/2 times the corresponding sides of the isosceles triangles.
Question 5. Draw a triangle ABC with side BC= 6 cm, AB= 5 cm and LABC =60°. Then construct a triangle whose sides are 3/4 of the corresponding sides of the triangle ABC.
Question 6. Draw a triangle ABC with side BC = 7 cm, LB = 45°, LA= 105°. Then, construct a triangle whose sides are 4/3 times the corresponding sides of MBC.
Question 7. Draw a right triangle in which the sides other than the hypotenuse are of lengths 4cm and 3cm. Then construct another triangle whose sides are 5/3 times the corresponding sides of the given triangle.
Exercise 11.2
In each of the following, given the justification of the construction.
Question 1. Draw a circle of radius 6 cm. From a point 10 cm away from its centre, construct a pair of tangents to the circle and measure their lengths.
Note: If centre of the circle is not given, then locate the centre first by taking two non parallel chords and then finding the point of intersection of their perpendicular bisectors.
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.
Question 3. Draw a circle of radius 3 cm. Take two points P and Q on one of its extended diameter and on opposite sides of its centre, each at a distance of 7 cm from its centre. Draw tangents to the circle from these two points P and Q.
Question 4. Draw a pair of tangents to a circle of radius 5 cm, which are inclined to each other at an angle of 60°.
Question 5. Draw a line segment AB of length 8 cm. Taking A as the centre, draw a circle of radius 4 cm and taking B as the centre, draw another circle of radius 3 cm. Construct tangents to each circle from the centre of the other circle.
Question 6. Let ABC be a right triangle in which AB= 6 cm, BC= 8 cm and LB= 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.
Question 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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