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Question
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.
Solution
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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