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प्रश्न
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.
उत्तर
Steps of construction :
(i) A 30 degree angle van be formed by knowing that the inverse sine of 0.5 is 30 degrees . In other words , a right triangle with a 30 degree angle has the hypotenuse twice as long as the leg opposite the near leg.
(ii) Using your compass, construct a 90° , then construct the leg opposite the 30 degree angle. Construct the hypotenuse twice as long , that makes a 30 degree angle.
(iii) Bisect 3 degree angle and you have 15 degrees,
(iv) From 90° cut off angle equal to 15° angle to get 75° angle. Bisect the 75° angle to get 37.5° angle.
(v) Now draw angle bisector of angle 37.5°.
(vi) On OR at 5 cm from O , drop a perpendicular PA from he angle bisector of angle 37.5°.
(vii) With PA as radius , draw a circle touching OA at A and OB at B.
This is the reqiured circle.
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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.
Using ruler and compasses only,
- Construct triangle ABC, having given BC = 7 cm, AB – AC = 1 cm and ∠ABC = 45°.
- Inscribe a circle in the ΔABC constructed in (i) above. Measure its radius.
Using ruler and compasses only,
- Construct a triangle ABC with the following data :
Base AB = 6 cm, BC = 6.2 cm and ∠CAB = 60°. - In the same diagram, draw a circle which passes through the points A, B and C and mark its center O.
- Draw a perpendicular from O to AB which meets AB in D.
- Prove that : AD = BD.
Construct a regular hexagon of side 4 cm. Construct a circle circumscribing the hexagon.
Using ruler and compasses only, construct a triangle ABC in which AB=S cm, BC=6 cm and CA=4.5 cm. Construct a circle passing through A, Band c.
Draw line segments OA = 4.5 cm, OB = 3.2 cm such that ∠ AOB = 45°. Construct a circle touching OA at A and passing through B.
Perpendicular bisectors of the sides AB and AC of a triangle ABC meet at O.
Does the perpendicular bisector of BC pass through O?
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.
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.
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.
