Construct an isosceles triangle whose base is 8 cm and altitude 4 cm and then another

triangle whose sides are $1 begin inline style 1 half end style$ times the corres ponding sides of the isosceles triangle.

Solution

Step of Construction :

(i) Draw a line segment BC = 8 cm.
(ii) Draw a perpendicular bisector AD (4 cm) of BC.
(iii) Joining AB and AC we get isosceles ΔABC.

(iv) Construct an acute ∠CBX downwards.
(v)    Along BX mark off 3 equal points B₁, B₂, B₃ such that BB₁ = B₁B₂ = B₂B₃.
(vi)    Join C to B₂ and draw a line through B₃ parallel to B₂C intersecting the extended line segment BC at C’.
(vii)    Again draw a parallel line C’ A’ to AC cutting BP at A’.
(viii)    ΔA ‘BC’ is the required triangle.
Justification :
C’A’ || CA [By construction] ΔABC ~ ΔA ‘BC’
[Using AA similarity condition]

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.

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Areas Related To Circles

Construct an isosceles triangle whose base is 8 cm and altitude 4 cm and then another

triangle whose sides are $1 begin inline style 1 half end style$ times the corres ponding sides of the isosceles triangle.

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.

Divide a line segment 11 cm in the ratio of 2 : 5 (a) internally (b) externally.

Mock Test Series

NCERT Sample Papers

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For Daily Free Study Material Join wiredfaculty

Areas Related To Circles

Construct an isosceles triangle whose base is 8 cm and altitude 4 cm and then another triangle whose sides are times the corres ponding sides of the isosceles triangle.

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.

Divide a line segment 11 cm in the ratio of 2 : 5 (a) internally (b) externally.

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

Construct an isosceles triangle whose base is 8 cm and altitude 4 cm and then another

triangle whose sides are $1 begin inline style 1 half end style$ times the corres ponding sides of the isosceles triangle.