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161.
Draw a line segment of length 8 cm and divide it internally in the ratio 4: 5.
Steps of construction.

1) Draw a line segment AB = 8 cm.
2) Draw a ray AX making an acute angle ∠BAX=60° with AB.
3) Draw a ray BY parallel to AX by making an acute angle ∠ABY=∠BAX.
4) Mark four points A₁, A₂, A₃, A₄ on AX and five points B₁,B₂,B₃,B₄,B₅ on BY in such a way that AA₁=A₁A₂=A₂A₃=A₃A₄.
5) Join A₄B₅
6) Let this line intersect AB at a point P.
Thus, P is the point dividing the line segment AB internally in the ratio of 4:5.

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Long Answer Type

162.

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163.

Draw a triangle ABC with BC = 6 cm, AB = 5 cm and ∠ABC 60. Then construct a triangle whose sides are 3/4 of the corresponding sides of the △ABC.

164.

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165.

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166.

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167.

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