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प्रश्न
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.
उत्तर
Steps of construction:
1) Draw an line segment BC = 5.2
2) With centre B and radius BA = 4.4 cm, draw an arc.
3) With C centre and radius CA = 7.1 cm, draw an arc intersecting the previous arc at A. Then ABC is the given triangle.
4) Draw the perpendicular bisectors of any two sides, say BC and AC, intersecting at O. Then O is the circumference of ΔABC.
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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.
Construct a ΔABC 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.
Using a ruler and compasses only:
1) Construct a triangle ABC with the following data: AB = 3.5 cm, BC = 6 cm and ABC = 120°
2) In the same diagram, draw a circle with BC as diameter. Find a point P on the circumference of the circle which is equidistant from AB and BC.
3) Measure ∠BCP.
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.
Using a ruler and compasses only:
- Construct a triangle ABC with the following data: AB = 3.5 cm, BC = 6 cm and ∠ABC = 120°.
- In the same diagram, draw a circle with BC as diameter. Find a point P on the circumference of the circle which is equidistant from AB and BC.
- Measure ∠BCP.
Draw a circle with radius 3 cm and inscribe an equilateral triangle in it.
Perpendicular bisectors of the sides AB and AC of a triangle ABC meet at O.
What is the relation between the distances OA, OB and OC?
Construct a triangle ABC in which AB = 5 cm, BC = 6.8 cm and median AD = 4.4 cm. Draw incircle of this triangle.
Using ruler and compass only, construct a triangle ABC such that AB = 5 cm, ABC = 75°, and the radius of the circumcircle of triangle ABC is 3.5 cm. On the same diagram, construct a circle, touching AB at its middle point and also touching the side AC.
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.
