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Three tangents are drawn at random to a given circle: Show that the odds are 3 to 1 against the circle being inscribed in the triangle formed by them.

solution: Prob of it being inscribed is equal to prob of all three pts of tangency not being on a semi circle = p = 1/4. Hence answer is (1-p)/p.

i dont understand how come 1/4 is coming?

maveric
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  • Is the solution something you were provided? Can you give some context, work you're already done, etc.? That said, HINT: how do you find the probability that when you flip two coins, none will come up heads? – Eric Snyder Jun 04 '22 at 05:25
  • none will come head means :HH TT HT TH SO 1/4 – maveric Jun 04 '22 at 05:31
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    I think your question is equivalent to the one asked here https://math.stackexchange.com/questions/268635/what-is-the-probability-that-the-center-of-the-circle-is-contained-within-a-tria – Anton V. Jun 04 '22 at 06:19
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    @maveric Right. Now how might you apply that to the circle case? Do you understand why the condition comes down to "the three tangent points are not in a semicircle"? – Eric Snyder Jun 06 '22 at 04:11
  • yes understood. – maveric Jun 11 '22 at 17:29

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