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ICSE Class 10 Mathematics Question 7 of 10

Long Answer Questions 2 — Question 7

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Question 116

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.)

Answer

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.

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. Maths Competency Focused Practice Questions Class 10 Solutions.

Hence, ∠BPC = 120°.