Mathematics
Construct a regular hexagon ABCDEF of side 4.3 cm and construct its circumscribed circle. Also, construct tangents to the circumscribed circle at points B and C which meets each other at point P. Measure and record ∠BPC.
(Use a ruler and a compass for this question.)
Constructions
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Answer
We know that each angle in a regular hexagon = 120°.
Draw a line segment AB = 4.3 cm.
At A and B draw rays making an angle of 120° each and cut off AF = BC = 4.3 cm.
At F and C, draw rays making angle of 120° each and cut off EF = CD = 4.3 cm.
Join ED. Hence, ABCDEF is the required hexagon.
Draw the perpendicular bisector of AB and AF. 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.
Draw the radius OB and OC.
At point B, construct a line perpendicular to OB. This line is the tangent at B.
At point C, construct a line perpendicular to OC. This line is the tangent at C.
The two tangents will intersect at point P.
Measure ∠BPC.
Hence, ∠BPC = 120°.
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