Mathematics
Using ruler and compasses only,
(i) Construct triangle ABC, having given BC = 7 cm, AB - AC = 1 cm and ∠ABC = 45°.
(ii) Inscribe a circle in the △ABC constructed in (i) above.
Answer
(i) Steps of construction :
Draw a line segment BC = 7 cm.
At B, draw a ray BX making an angle of 45° and cut off BE = AB - AC = 1 cm.
Join EC and draw the perpendicular bisector of EC intersecting BX at A.
Join AC.
Hence, ABC is the required triangle.
(ii) Steps of construction :
Draw angle bisectors of ∠ABC and ∠ACB intersecting each other at O.
From O, draw perpendicular OL to BC.
With O as center and OL as radius draw a circle, touching sides of △ABC. Measure OL.
On measuring,
OL = 1.8 cm.
Hence, above is the required incircle of △ABC with radius = 1.8 cm.
Related Questions
Using ruler and compasses only construct a triangle ABC in which BC = 4 cm, ∠ACB = 45° and perpendicular from A on BC is 2.5 cm. Draw a circle circumscribing the triangle ABC.
Draw a circle of radius 5 cm. Draw two tangents to this circle so that the angle between tangents is 45°.
Using ruler and compasses only, draw an equilateral triangle of side 4.5 cm and draw its circumscribed circle. Measure the radius of the circle.
Using ruler and compasses only,
(i) Construct a triangle ABC with the following data :
Base AB = 6 cm, BC = 7.5 cm and angle CAB = 60°.
(ii) In same diagram, draw a circle which passes through the points A, B and C and mark its center O.
(iii) Draw a perpendicular from O to AB which meets AB in D.
(iv) Prove that : AD = BD.