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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.

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.

Steps of constructions:

1) Draw BC = 7 cm.

At B, construct ∠CBX = 45° and at C, construct

∠BCY = 180 - (45 + 105) = 30°

3) Let BX and CY intersect at A, &DElta; ABC so obtained is the given triangle.

4) Construct an acute angle Δ CBZ at B on opposite side of vertex A of δ ABC.

5) Mark-off four points ( greater of 4 and 3 in 3/4 points B_1,B_2,B₃,B₄ on BZ such that BB₁ = B₁B₂ = B₂B₃ = B₃B_4.

6) Join B₄ to C.

7) Draw B₃C' parallel to B₄C which meets BC at C'.

8) From C', draw C'A' parallel to CA meeting at A'.

Thus, $∆$ A'BC' is the required triangle, each of whose side is $\frac{3}{4}$ times

the corresponding sides of $∆ABC.$

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.