Use ruler and compass for the following construction. Construct a ΔABC, where AB = 6 cm, AC = 4.5 cm and ∠BAC = 120°. Construct a circle circumscribing the ΔABC. Measure and write down the length of the radius of the circle.
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Given,
AB = 6 cm, AC = 4.5 cm and ∠BAC = 120°
Steps of construction,
Draw a line segment AB = 6 cm.
Construct ∠BAY = 120°.
With A as center and radius equal to 4.5 cm draw an arc intersecting AY at C.
Join points B and C.
Draw the perpendicular bisectors of AB and AC. The point where the two perpendicular bisectors intersect is the center of the circumscribing circle. Mark this point as O.
Measure OC, with O as center and OC as radius, construct a circle passing through points A, B and C.
On measuring, we get :
OC = 5.2 cm
Hence, radius of circle = 5.2 cm.