Exercise 11.1 7 Questions – Dividing a Line Segment
Draw a line segment of length 7.6 cm and divide it in the ratio 5:8. Measure the two parts.
Steps:
1. Draw AB = 7.6 cm.
2. Draw ray AX at acute angle to AB.
3. Mark 5+8 = 13 equal points Aâ‚, Aâ‚‚, ..., Aâ‚₃ on AX.
4. Join Aâ‚₃ to B.
5. Draw line through Aâ‚… parallel to Aâ‚₃B intersecting AB at C.
6. AC:CB = 5:8. AC ≈ 2.9 cm, CB ≈ 4.7 cm
Similar construction steps for: 4 cm in 1:1 (bisect), 8 cm in 3:5, 10 cm in 3:4, 5.6 cm in 4:7, constructing triangles with given sides (scale factor application), and 5 cm in 8:5.
Exercise 11.2 7 Questions – Tangents & Similar Triangles
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.
Steps:
1. Draw circle with centre O, radius 6 cm.
2. Mark P at distance OP = 10 cm.
3. Draw perpendicular bisector of OP. Let M be midpoint.
4. With centre M, radius MO, draw circle intersecting given circle at Q and R.
5. Join PQ and PR – these are the required tangents.
6. Tangent length = √(10²âˆ'6²) = 8 cm
Q2: Construct a triangle similar to given Î"ABC with sides 4 cm, 5 cm, 6 cm and then a similar triangle with scale factor 2/3.
1. Draw Î"ABC with given sides. 2. Draw ray BX at acute angle. 3. Mark Bâ‚,Bâ‚‚,B₃. 4. Join B₃ to C. 5. Draw line through Bâ‚‚ ∥ B₃C intersecting BC at C'. 6. Draw C'A' ∥ CA. Î"A'BC' is similar with scale factor 2/3.
Q4: Construct an isosceles triangle with base 8 cm and altitude 4 cm. Construct similar triangle with scale factor 1½ (enlargement).
Q5: Draw Î"ABC with BC=6 cm, AB=5 cm, ∠ABC=60°. Construct a similar triangle with sides 3/4 of corresponding sides.
Q6: Draw circle of radius 3 cm. Take two points P and Q on one of its extended diameters each at distance 7 cm from centre. Draw tangents. â†' Same method as Q1, tangent length = √(49âˆ'9)=√40=2√10 cm.
Q7: Draw a pair of tangents to a circle of radius 5 cm inclined to each other at an angle of 60°. â†' The angle between radii to points of contact = 120°. Draw radii at 120°, then construct perpendiculars.
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