Mathematics
Draw a regular hexagon of side 3.5 cm. Construct its circumcircle and measure its radius.
Answer
We know that each angle in a regular hexagon = 120°.
Draw a line segment AB = 3.5 cm.
At A and B draw rays making an angle of 120° each and cut off AF = BC = 3.5 cm.
At F and C, draw rays making angle of 120° each and cut off EF = CD = 3.5 cm.
Join ED. Hence, ABCDEF is the required hexagon.
Draw the perpendicular bisector of AB and BC. Let these bisectors meet at the point O.
With O as center and radius equal to OA or OB, draw a circle which passes through the vertices of the hexagon. This is the required circumcircle of hexagon ABCDEF.
On measuring we get OA = 3.5 cm.
Hence, the required hexagon with circumcircle of radius 3.5 cm. is formed.
Related Questions
Construct a triangle ABC with the following data :
AB = 5 cm, BC = 6 cm and ∠ABC = 90°.
(i) Find a point P which is equidistant from B and C and is 5 cm from A. How many such points are there ?
(ii) Construct the inscribed circle of △ABC drawn above.
Using ruler and compasses only, construct an equilateral triangle of height 4 cm and draw its circumcircle.
Draw a triangle ABC, given that BC = 4 cm, ∠C = 75° and that radius of circumcircle of △ABC is 3 cm.
Using ruler and compasses only :
(i) Construct a triangle ABC with the following data :
BC = 7 cm, AB = 5 cm and ∠ABC = 45°.
(ii) Draw the inscribed circle to △ABC drawn in part (i).