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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.

Steps of Construction :
1.    Draw a line segment AB = 5 cm.
2.    At A make ∠BAY = 45°.
3.    Take A as centre and radius = AC = 6 cm (= CA), draw an arc cutting AY at C.
4.    Join BC to obtain the triangle ABC.
5.    Draw any ray AX making an acute angle with AB on the side opposite to the vertex
C.
6.    Mark off 6 points (the greater of 6 and 5 in 6/5) A₁, A₁, A₃, A₄,A₅ and A₆ on AX so
that
AA₁ = A₁A₂ = A₂A₃ = A₃A₄ = A₄A₅ = A₅A₆7.    Join A₅ (the 5th point, being the smaller of 5 and 6 in 5/6) to B and draw a line through A₆ parallel to A₅B intersecting the extended line segment AB at B’.
8.    Draw a line through B‘C’ parallel to BC intersecting the extended line segment AC at C’.
Thus, AB ‘C’ is the required triangle

Steps of Construction :1. Draw a line segment AB = 5 cm.2.

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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.

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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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