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Math Help - (Another) Grade 11 High School Circles Question

  1. #1
    s3a
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    (Another) Grade 11 High School Circles Question

    "Isosceles triangle ABC is inscribed in a circle with radius 5cm. Base BC measures 8cm. Find the length of the other two sides of the triangle."

    Answer:
    4Sqrt(5)cm or ~ 8.94cm

    Can someone show it to me visually so that I know how to interpret the question because when I do it, I get a different answer.
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  2. #2
    A riddle wrapped in an enigma
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    Quote Originally Posted by s3a View Post
    "Isosceles triangle ABC is inscribed in a circle with radius 5cm. Base BC measures 8cm. Find the length of the other two sides of the triangle."

    Answer:
    4Sqrt(5)cm or ~ 8.94cm

    Can someone show it to me visually so that I know how to interpret the question because when I do it, I get a different answer.
    See diagram.

    Drop a perpendicular from the vertex angle to the base which bisects the base.

    Use the Pythagorean theorem to find the distance from the center to the base.

    5^2=4^2+x^2

    25-16=x^2

    9=x^2

    x=3 This is the length of the altitude.

    Use Pythagorean theorem again to find AC.

    (AC)^2=4^2+8^2

    (AC)^2=80

    AC=\sqrt{80}

    AC=\sqrt{16\cdot 5}

    AC=4\sqrt{5}
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