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Constructions (Circles) — Mathematics STD 10 — Question

ICSE BoardEnglish MediumSTD 10MathematicsConstructions (Circles)5 Marks
Question
Using ruler and compasses only,
(i) Construct triangle ABC, having given BC = 7cm, AB – AC = 1cm and ∠ABC = 45°.
(ii) Inscribe a circle in the ΔABC constructed in (i) above. Measure its radius.
✓

Answer

  
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 45o and cut off BE = AB − AC = 1cm
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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