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Triangle ABC is inscribed in a circle, such that AC is a diameter of t
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10 Feb 2023, 06:10
10 Feb 2023, 06:10
Expert Reply
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Question Stats:
80% (01:26) correct
20% (00:15) wrong based on 5 sessions
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Triangle ABC is inscribed in a circle, such that AC is a diameter of the circle (see figure). What is the circumference of the circle?
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\(17 \pi\)
Re: Triangle ABC is inscribed in a circle, such that AC is a diameter of t
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20 Feb 2023, 07:16
20 Feb 2023, 07:16
Expert Reply
OE
If AC is a diameter of the circle, then inscribed triangle ABC is a right triangle, with AC as the hypotenuse. Therefore, you can apply the Pythagorean theorem to find the length of AC:
\(8^2+15^2=(AC)^2\)
AC=17
AC is the diameter of the circle, so d = 17. The circumference of the circle is \(\pi d\), or \(17 \pi\).
If AC is a diameter of the circle, then inscribed triangle ABC is a right triangle, with AC as the hypotenuse. Therefore, you can apply the Pythagorean theorem to find the length of AC:
\(8^2+15^2=(AC)^2\)
AC=17
AC is the diameter of the circle, so d = 17. The circumference of the circle is \(\pi d\), or \(17 \pi\).
gmatclubot
Re: Triangle ABC is inscribed in a circle, such that AC is a diameter of t [#permalink]
20 Feb 2023, 07:16
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