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प्रश्न
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.
उत्तर
Steps of construction:
i. Construction of triangle:
a. Draw a line segment BC = 7 cm.
b. At B, draw a ray BX making an angle of 45° and cut off BE = AB − AC = 1 cm.
c. Join EC and draw the perpendicular bisector of EC intersecting BX at A.
d. Join AC.
ΔABC is the required triangle.
ii. Construction of incircle:
e. Draw angle bisectors of ∠ABC and ∠ACB intersecting each other at O.
f. From O, draw perpendiculars OL to BC.
g. O as centre and OL as radius draw circle which touches the sides of the ΔABC.
This is the required in-circle of ΔABC.
On measuring, radius OL = 1.8 cm.
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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 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 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 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 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.
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.
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.
