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प्रश्न
Construct a regular hexagon of side 4 cm. Construct a circle circumscribing the hexagon.
उत्तर
Steps of construction:
- Draw a circle of radius 4 cm with centre O.
- Since the interior angle of regular hexagon is 60°, draw radii OA and OB such that ∠AOB = 60°.
- Cut off arcs BC, CD, EF and each equal to arc AB on given circle.
- Join AB, BC, CD, DE, EF, FA to get required regular hexagon ABCDEF in a given circle.
The circle is the required circumcircle, circumscribing the hexagon.
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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.
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
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.
Using ruler and compasses only, construct Δ ABC in which BC=7.5 cm, ∠ ABC = 60° and AC - AB= 1.5 cm. Inscribe a circle in the Δ ABC and measure its radius.
Draw a circle with radius 3 cm and inscribe an equilateral triangle in it.
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.
Draw a circle of radius 4.5 cm. Take a point Pon its circumference. Construct a tangent to the circle at P without using the centre.
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 ΔABC with base BC = 3.5 cm, vertical angle ∠ BAC = 45°, and median through the vertex A is 3.5 cm. Write also the steps of construction.
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.
