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Constructions

Short Answer Type

161.

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

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Long Answer Type

162.

Construct an isosceles triangle with base 8 cm and altitude 4 cm. Construct another triangle whose sides are 2/3 times the corresponding sides of the isosceles triangle.

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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.

(i) Draw a line segment BC = 6 cm, draw a ray BX making 60° with BC.
(ii) Draw an arc with radius 5 cm from B so that it cuts BX at A.
(iii) Now join AC to form △ABC.
(iv) Draw a ray by making an acute angle with NC opposite to vertex A.
(v) Locate 4 points B₁, B₂, B₃, B₄, on by such that BB₁ = B₁B₂ = B₂B₃ = B₃B₄
(vi) Join B₄C and now draw a line from B₃ parallel to BC₄ so that it cuts BC at C'.
(vii) From C' draw a line parallel to AC and cuts AB at A'.
(viii) △A'BC' is the required triangle.

164.

Construct a tangent of a circle of radius 4 cm from a point on the concentriccircle of radius 6 cm.

165.

Draw a line segment AB of length 8 cm. Taking A as centre, draw a circle of radius 4 cm and taking B as centre, draw another circle of radius 3 cm. Construct tangents to each circle from the centre of the other circle.

166.

Construct a triangle ABC with side BC = 7 cm, ∠B = 45°, ∠A = 105°. Then construct another triangle whose sides are 3/4 times the corresponding sides of the Δ ABC.

167.

Draw a triangle ABC with side BC = 6 cm, $∠$ C = 30⁰ and $∠$ A = 105⁰. Then construct another triangle whose sides are $\frac{2}{3}$ times the corresponding sides of $∆$ ABC.