Mathematics
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.
Constructions
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Answer
Steps of construction :
Draw a line segment BC = 4 cm.
At C, draw a perpendicular line CX and from it, cut off CE = 2.5 cm.
From E, draw EY, perpendicular to CX.
From C, draw a ray making an angle 45° with CB, which intersects EY at A.
Join AB. Hence, ABC is the required triangle.
Draw perpendicular bisectors of sides AB and BC intersecting each other at O.
With center O, and radius OA or OB or OC draw a circle passing through A, B and C. Measure OB.
On measuring,
OB = 2 cm.
Hence, above is the required circumcircle of △ABC with radius = 2 cm.
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