Hexagon Problem #2

hexagon 2

AB and BC are tangents to the circle, touching it at points A and C.

If the circumference of the circle is 42πcm, find the area of the hexagon.

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10 thoughts on “Hexagon Problem #2

  1. The diagram is geometrically impossible as drawn. If AD ⊥ AB (tangent is perpendicular to radius) and CD ⊥ CB, and ∠D is 120 (regular hexagon), then the angle indicated by the dashed lines (∠B) must be 60. Another way to describe the problem is that either a regular hexagon is circumscribed about the circle (which you don’t seem to intend), or it’s not tangent to the circle at non-adjacent vertices A and C (which the “not to scale” drawing reveals).

  2. Howard, that comment confused me for ages! Mainly because I was staring at the (inaccurate, but now adjusted) diagram instead of thinking about the maths. Many thanks. Can I nominate you as my puzzle verifier before posting in future? My wife is giving birth soon so I fear I may have baby brain over the next few months! 🙂

  3. Enjoyed doing this one – less tricky than the ones on subject days! Going to give it to my Year 12 c1 pupils tomorrow and see how they do 🙂

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