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Mathematics

Draw an inscribing circle of regular hexagon of side 5.8 cm.

Constructions

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Answer

Each interior angle of a regular hexagon = (2n5n)×90°\Big(\dfrac{2n - 5}{n}\Big) \times 90°

=2×646×90°=8×15°=120°.= \dfrac{2 \times 6 - 4}{6} \times 90° \\[1em] = 8 \times 15° \\[1em] = 120°.

Steps of construction :

  1. Draw a regular hexagon ABCDEF with each side equal to 5.8 cm and each interior angle = 120°.

  2. Draw the bisectors of interior angles at A and B which intersect each other at point I.

  3. From point I , draw IP perpendicular to AB.

  4. With I as center and IP as radius, draw a circle which will touch all the sides of the regular hexagon drawn.

Hence, above is the required incircle of regular hexagon.

Draw an inscribing circle of regular hexagon of side 5.8 cm. Constructions, Concise Mathematics Solutions ICSE Class 10.

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