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प्रश्न
Using ruler and compass only, construct a ΔABC such that BC = 5 cm and AB = 6.5
cm and ∠ABC = 120°
1) Construct a circum-circle of ΔABC
2) Construct a cyclic quadrilateral ABCD, such that D is equidistant from AB and BC.
उत्तर
Steps of construction:
1) Draw a line segment BC of length 5 cm.
2) At B, draw a ray BX making an angle of 120° with BC.
3) With B as centre and radius 6.5 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 ΔABC
6) Draw the angle bisector of ∠ABC
7) The angle bisector of ABC and let it meet circle at point D.
8) Join AD and DC to obtain the required cyclic quadrilateral ABCD such that point D is equidistant from AB and BC.
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संबंधित प्रश्न
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.
Using ruler and compasses only, draw an equilateral triangle of side 5 cm. Draw its inscribed circle. Measure the radius of the circle.
Construct a regular hexagon of side 4 cm. Construct a circle circumscribing the hexagon.
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.
Contruct 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 incricle.
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 of radius 4.5 cm. Take a point Pon its circumference. Construct a tangent to the circle at P without using the centre.
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 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.
