Circles

SAT Math· difficulty 5/5

A triangle inscribed in a circle has an inscribed angle of 40°40° that intercepts an arc. The radius of the circle is 9. What is the length of this arc?

  • A

    4π4\pi

    check_circle
  • B

    4π9\frac{4\pi}{9}

  • C

    2π2\pi

  • D

    8π8\pi

Explanation

Intercepted arc =2(40°)=80°= 2(40°) = 80°. Arc length =frac80360(2pi)(9)=frac29(18pi)=4pi= \\frac{80}{360}(2\\pi)(9) = \\frac{2}{9}(18\\pi) = 4\\pi.

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