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प्रश्न
Construct a triangle ABC in which base BC = 6 cm, AB = 5.5 cm and ∠ABC = 120°.
Construct a circle circumscribing the triangle ABC.
Draw a cyclic quadrilateral ABCD so that D is equidistant from B and C.
उत्तर
Steps of construction:
1) Draw a line segment BC of length 6 cm.
2) At B, draw a ray BX making an angle of 120 with BC.
3) With B as centre and radius 5.5 cm, draw an arc to cut the ray BX at A. Join AC.
ΔABC will be obtained.
4) Draw the perpendicular bisectors of AB and BC to meet at point O.
5) With O as centre and radius OA, draw a circle. The circle will circumscribe ∠ABC.
6) Draw the angle bisector of ∠ABC.
7) The angle bisector of ∠ABC and the perpendicular bisector of line segment BC will
intersect at point D. Point D will be equidistant from points B and C.
8) Join AD and DC to obtain the required cyclic quadrilateral ABCD.
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संबंधित प्रश्न
Using a ruler and a compass, construct a triangle ABC in which AB = 7 cm, ∠CAB = 60° and AC = 5 cm. Construct the locus of :
- points equidistant from AB and AC.
- points equidistant from BA and BC.
Hence construct a circle touching the three sides of the triangle internally.
Use ruler and compasses only for the following questions. All constructions lines and arcs must be clearly shown
Construct a ABC in which BC = 6.5 cm, ABC = 60°, AB = 5 cm.
In the figure given below 'O' is the centre of the circle. If QR = OP and ∠ORP = 20°. Find the value of 'x' giving reasons
Perpendicular bisectors of the sides AB and AC of a triangle ABC meet at O.
- What do you call the point O?
- What is the relation between the distances OA, OB and OC?
- Does the perpendicular bisector of BC pass through O?
Draw a line segment OA , 5 cm long. AT O , using ruler and compasses only, construct OB such that , ∠ AOB = 37.5° construct a circle to touch OA at A and to touch OB at B.
Construct a triangle ABC in which AB = 5 cm, BC = 6.8 cm and median AD = 4.4 cm. Draw incircle of this triangle.
Construct a triangle whose sides are 4.4 cm, 5.2 cm, and 7.1 cm. Construct its circumcircle. Write also the steps of construction.
Construct a Δ ABC with BC = 6.5 cm, AB = 5.5 cm, AC = 5 cm. Construct the incircle of the triangle. Measure and record the radius of the incircle.
Use ruler and compasses only for this question:
(i) Construct A ABC, where AB = 3.5 cm, BC = 6 cm and ∠ ABC = 60°.
(ii) Construct the locus of points inside the triangle which are equidistant from BA and BC.
(iii) Construct the locus of points inside the triangle which are equidistant from B and C.
(iv) Mark the point P which is equidistant from AB, BC, and also equidistant from B and C. Measure and record the length of PB.
Ruler and compasses only may be used in this question. All constructions lines and arcs must be clearly shown, and the be sufficient length and clarity to permit assessment:
(i) Construct a triangle ABC, in which AB = 9 cm, BC = 10 cm and angle ABC = 45°.
(ii) Draw a circle, with center A and radius 2.5 cm. Let it meet AB at D.
(iii) Construct a circle to touch the circle with center A externally at D and also to touch the line BC.
