Question

(Use a ruler and a compass for this question.)

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.

Answer 1

We know that each angle in a regular hexagon = 120°.

1. Draw a line segment AB = 4.3 cm.
2. At A and B draw rays making an angle of 120° each and cut off AF = BC = 4.3 cm.
3. At F and C, draw rays making angle of 120° each and cut off EF = CD = 4.3 cm.
4. Join ED. Hence, ABCDEF is the required hexagon.
5. Draw the perpendicular bisector of AB and AF. Let these bisectors meet at the point O.
6. 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.
7. Draw the radius OB and OC.
8. At point B, construct a line perpendicular to OB. This line is the tangent at B.
9. At point C, construct a line perpendicular to OC. This line is the tangent at C.
10. The two tangents will intersect at point P.
11. Measure ∠BPC.

Hence, ∠BPC = 120°.