Mathematics
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.
Answer
Steps of Construction :
Draw a line segment BC = 4.5 cm.
With centers B and C, draw two arcs of radius 4.5 cm which intersect each other at A.
Join AC and AB.
Draw perpendicular bisectors of AC and BC intersecting each other at O.
With center O, and radius OA or OB or OC draw a circle which pass through A, B and C. Measure OC.
On measuring, OC = 2.6 cm.
Hence, above is the required circumcircle with radius 2.6 cm.
Related Questions
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.
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.
Draw a circle of radius 5 cm. Draw two tangents to this circle so that the angle between tangents is 45°.
Draw a circle of radius 3 cm. Mark a point P at a distance of 5 cm from the center of the circle drawn. Draw two tangents PA and PB to the given circle and measure the length of each tangent.