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Constructions

Long Answer Type

91. Construct a ΔABC in which CA = 6 cm, AB = 5 cm and ∠BAC = 45°, then construct a triangle similar to the given triangle whose sides are 6/5 of the corresponding sides of the ΔABC.

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Short Answer Type

92.

Construct a triangle similar to given ABC in which AB = 4 cm, BC = 6 cm and ∠ABC = 60°, such that each side of the new triangle is 3/4 of given Δ ABC.

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93. Construct a Δ ABC in which AB = 6.5 cm, ∠B = 60° and BC = 5.5 cm. Also construct a triangle AB‘C’ similar to ΔABC, whose each side is 3/2 time. The coresponding sides of triangle ABC

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94. Draw a circle of radius 3 cm. From a point 5 cm away from its centre, construct the pair of tangents to the circle.

Steps of Construction :

(i) Construct a circle C₁ (say) of radius 3 cm.
(ii)    P is a point 5 cm away from the centre of circle C₁.
(iii)    Join OP.
(iv)    Draw ⊥ bisector of OP which intersects OP at M.

Steps of Construction :
(i) Construct a circle C1 (say) of radius 3

(v)    Taking M as centre and OM as radius draw a circle which intersects the circle C₁at A and B.
(vi)    Join PA and PB
(vii)    On, measuring we find PA = PB = 4 cm. Thus PA and PB are the required tangents.

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95. Construct a circle whose radius is equal to 4 cm. Let P be a point whose distance from its centre is 6 cm. Construct two tangents to it from P.

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96. Draw a line segment AB = 4.8 cm and divide it internally in the ratio 3 : 5.

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97. Draw a line segment MN = 3cm and divide it exterally in the ratio of 3 : 2.

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98. Draw a line segment AB = 4 cm and divide it externally in the ratio of 5 : 3.

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99. Determine a point which divides a line segment of length 10 cm internally in the ratio 2 : 3.

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100.

Draw a line segment 4.5 cm long and divide it internally in the ratio 2 : 3. Measure each part.

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