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प्रश्न
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.
उत्तर
Steps of construction:
- Draw a line segment BC = 6 cm.
At B, draw a ray BX making an angle of 120° with BC. with B as center and radius 3.5 cm, out off AB = 3.5 cm. Join AC
Thus, ABC is the required triangle. - Draw perpendicular bisector MN of BC at point O. With O as center and radius = OB, draw a cirde.
Draw angle bisector of ∠ABC which meets the circle at point P.
Thus, point P is equidistant from AB and BC. - On mesuring, ∠BCP = 30°
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संबंधित 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.
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.
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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.
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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.
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Does the perpendicular bisector of BC pass through O?
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.
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