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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
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.
In the figure given below 'O' is the centre of the circle. If QR = OP and ∠ORP = 20°. Find the value of 'x' giving reasons
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 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.
Contruct 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 incricle.
Using ruler and compasses only, construct Δ ABC in which BC=7.5 cm, ∠ ABC = 60° and AC - AB= 1.5 cm. Inscribe a circle in the Δ ABC and measure its radius.
Construct a triangle ABC in which AB = 5 cm, BC = 6.8 cm and median AD = 4.4 cm. Draw incircle of this triangle.
Use ruler and compasses only for this question:
(i) Construct A ABC, where AB = 3.5 cm, BC = 6 cm and ∠ ABC = 60°.
(ii) Construct the locus of points inside the triangle which are equidistant from BA and BC.
(iii) Construct the locus of points inside the triangle which are equidistant from B and C.
(iv) Mark the point P which is equidistant from AB, BC, and also equidistant from B and C. Measure and record the length of PB.
