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प्रश्न
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.
उत्तर
Steps of construction:
1) Draw a line segment BC = 3 cm and make ∠ CBP = 45°
2) Construct EB ⊥ BP.
3) Draw the perpendicular bisector of BC its intersecting BE in O and BC in D.
4) Draw a circle taking O as a centre and OB as the radius.
5) Now with D as centre and radius = 3.5 cm. draw arcs of the circle intersecting the above-drawn circle in A and A'.
6) Join AB, AC and A'B, A'C.
Then the Δs, ΔABC and ΔA'BC are the required triangles.
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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.
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 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.
Perpendicular bisectors of the sides AB and AC of a triangle ABC meet at O.
- What do you call the point O?
- What is the relation between the distances OA, OB and OC?
- Does the perpendicular bisector of BC pass through O?
Using ruler and compasses only, construct and equilateral triangle with side 4.5 cm. Draw a circumcircle of this triangle 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.
Construct a triangle ABC in which AB = 5 cm, BC = 6.8 cm and median AD = 4.4 cm. Draw incircle of this triangle.
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.
