marigirl
  • marigirl
Working on a Differentiation question- need some advice. The Question: A circle has a diameter AB of length 8cm. C is a point on the circumference. Show that the triangle ABC will be isosceles if the perimeter is a maximum and find the maximum perimeter. My solution so far: Since length AB is the diameter, then Angle ACB is 90 degrees. We can use Pythagoras Theorem to express the perimeter of this triangle.
Mathematics
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chestercat
  • chestercat
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marigirl
  • marigirl
Length of sides of triangle is a b and 8 \[side b= \sqrt{64-a ^{2}}\] Perimeter = 8+ a+b \[P= 8+a+\sqrt{64-a ^{2}}\] then I derived this equation \[\frac{ dP }{ da }= 1-\frac{ a }{ \sqrt{64-a ^{2}} }\] then made this equation equal to zero to find maximum \[a=4\sqrt{2}\] Then Used this Value to find Maximum Perimeter Maximum perimeter value is 19.3cm MY QUESTION: How do I actually write up that I have Triangle ABC is isosceles.?
marigirl
  • marigirl
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anonymous
  • anonymous
hmmm just guess.. AC = CB ?

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marigirl
  • marigirl
When I went about calculating the perimeter, I did go about saying side a and side b and side c which is 8cm..... but I am not sure how to mathematically state that what I found is isosceles. (My answer matches up with the model answers provided)
anonymous
  • anonymous
I see what you mean, Im not sure what the expectation is of your teacher, but I would think if you proved AB <> AC and AC = CB then triangle ABC is isosceles by the isosceles theorem
marigirl
  • marigirl
oh yes i see it.. i did calculate a and then from that i can get b .. both these lengths are the same .. so i guess that is sufficient enough..

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