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प्रश्न
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.
उत्तर
Steps of construction:
- Draw a line segment AB = 6 cm
- At A, draw a ray making an angle of 60° with BC.
- With B as centre and radius = 6.2 cm draw an arc which intersects AX ray at C.
- Join BC.
ΔABC is the required triangle. - Draw the perpendicular bisectors of AB and AC intersecting each other at O.
- With centre O, and radius as OA or OB or OC, draw a circle which will pass through A, B and C.
- From O, draw OD ⊥ AB.
Proof: In right ΔOAD and ΔOBD
OA = OB ...(Radii of same circle)
Side OD = OD ...(Common)
∴ ΔOAD ≅ ΔOBD ...(R.H.S.)
`=>` AD = BD ...(C.P.C.T.)
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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 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 incircle.
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 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.
Construct Δ ABC in which AB = 5 cm, BC = 4. 5 cm and ∠ ABC = 60" .. Construct a cirde to circumscribe. Δ ABC.
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 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.
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.
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.
