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in enter image description here

In the above image, is there a specific theorem that can be used to state which of the four statements must be true for x?

DonAntonio
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bagrut1
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  • The part of $;a;$ inside the circle must be less that a diameter (which is a maximal chord in any circle) as we're told that that line doesn't pass through $;\mathcal O;$ ,so... – DonAntonio Jun 16 '19 at 21:29
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    Thus, answer (1). Thank you. Would there be a way of calculating the exact measurement? – bagrut1 Jun 16 '19 at 21:32
  • True, hence the answer is (1). I was just asking for my own edification, but I'm assuming the answer is in the negative. Thank you! – bagrut1 Jun 16 '19 at 21:36
  • No, there is no way of calculating the exact answer. – John Wayland Bales Jun 16 '19 at 21:38

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The chord labeled $a$ is shorter than the diameter which is $4\text{ cm}$. One segment of this chord is given as $1.5\text{ cm}$, so by difference the remains segment must be ... Uh-oh, gotta run. Can you finish?

Oscar Lanzi
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