Areas Related to Circles

Question

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 $bold 3 over bold 4$ of given ΔABC.

Solution

Steps of Construction :

1.    Draw a line segment BC = 6 cm.
2.    At B make ∠CBY = 60°.
3.    Take B as centre and radius = AB = 4 cm, draw an arc cutting BY at A.
4.    Join CA to obtain the triangle ABC.
5.    Draw any ray BX making an acute angle with BC on the opposite side of the vertex A.
6.    Mark off 4 (the greater of 3 and 4 in 3/ 4) points B₁, B₂, B₃ and B₄ on BX so that
BB₁ = B₁B₂ = B₂B₃ = B₃B₄

7. Join B₄C and draw a line through B₃ (the third point, 3 being smaller of 3 and 4 in 3/4), parallel to B₄C to intersect BC at C’.
8. Draw a line through C’ parallel to the line CA to intersect BA at A’ (see Fig.) Thus, ΔA ‘BC’ is the required triangle.

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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 $bold 3 over bold 4$ of given ΔABC.

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Areas Related To Circles

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 of given ΔABC.

Some More Questions From Areas Related to Circles Chapter

Draw a circle of radius 6 cm. From a point 10 cm away from its centre, construct the pair of tangents to the circle and measure their lengths.

Draw a circle of radius 3 cm. Take two points at a distance 7 cm from its centre. Draw tangents to the circle from these two points P and Q.

Draw a pair of tangents to a circle of radius 5 cm which are inclined to each other at an angle of 60°.

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.

Let ABC be a right angle in which AB = 6 cm, BC = 8 cm and ∠B = 90°. BD is the perpendicular from B on AC. The circle through B, C, D is drawn. Construct the tangents from A to this circle.

Draw a circle with the help of a bangle. Take a point outside the circle. Construct the pair of tangents from this point to the circle.

Draw a line segment of length 7.6 cm and divide it in the ratio 3 : 5.

Divide the given line segment AB of length 6 cm internally in the ratio 3 : 4.

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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 $bold 3 over bold 4$ of given ΔABC.