Construct a triangle of sides 4 cm, 5 cm and 6 cm and then a triangle similar to it whose sides arc $2 over 3$ of the corresponding sides of the first triangle.

Solution

Steps of Construction :

(i) Construct a ΔABC in which AB = 6 cm, AC = 4 cm, BC = 5 cm.
(ii)    At A draw an acute ∠BAX below base AB.
(iii)    Along AX mark off points A₁, A₂, A₃ such that AA₁ = A₁ A₁ = A₂ A₃.
(iv)    Join A₃B.
(v)    From A₂ draw A₂B’ || A₃B meeting AB at B’.
(vi)    From B’ draw B‘C’ || CB meeting AC at C’. Thus, ΔAB‘C’ is the required triangle, each of whose sides is (2/3)rd of the corresponding sides of the ΔABC.
Justification :

[From (i)]
[By Basic proportionality theorem)

Some More Questions From Areas Related to Circles Chapter

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

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.

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Areas Related To Circles

Construct a triangle of sides 4 cm, 5 cm and 6 cm and then a triangle similar to it whose sides arc $2 over 3$ of the corresponding sides of the first triangle.

Some More Questions From Areas Related to Circles Chapter

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

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.

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For Daily Free Study Material Join wiredfaculty

Areas Related To Circles

Construct a triangle of sides 4 cm, 5 cm and 6 cm and then a triangle similar to it whose sides arc of the corresponding sides of the first triangle.

Some More Questions From Areas Related to Circles Chapter

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

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.

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

Construct a triangle of sides 4 cm, 5 cm and 6 cm and then a triangle similar to it whose sides arc $2 over 3$ of the corresponding sides of the first triangle.