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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.

$Steps of consrtuctions : 1 . Draw two cocentric circl e with centre O and radii 4 cm and 6 cm . Take a point P on the outer circle and then join OP . 2 . Draw the perpendicular bisector of OP . Let the bisector intersects Op at M . 3 . With M as the centre and OM as the radius, draw a circle . Let it intersect the inner circle a t A and B 4 . Join PA and PB . Therefore, PA and PB are the required tangents .$

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.