Mathematics
Using ruler and compasses only, construct a triangle ABC in which BC = 4 cm, ∠ACB = 45° and the perpendicular from A on BC is 2.5 cm. Draw the circumcircle of triangle ABC and measure its radius.
Answer
Steps of construction :
Draw a line segment BC = 4 cm.
At B, draw a perpendicular and cut off BE = 2.5 cm.
From E, draw a line EF parallel to BC.
From C, draw a ray making an angle of 45° which intersects EF at A.
Join AB.
Draw a line AD parallel to BE. This AD is the perpendicular bisector of BC.
Draw the perpendicular bisectors of sides BC and AC intersecting at O.
With centre O and radius OB or OC or OA draw a circle which will pass through A, B and C. This is the circumcircle of △ABC.
On measuring OB we get the radius of the circumcircle.
Hence, the radius of circumcircle = 2 cm.
Related Questions
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